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A structure preserving numerical method for the ideal compressible MHD system J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-16 Tuan Anh Dao, Murtazo Nazarov, Ignacio Tomas
We introduce a novel structure-preserving method in order to approximate the compressible ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD equations using a non-divergence formulation, where the contributions of the magnetic field to the momentum and total mechanical energy are treated as source terms. Our approach uses the Marchuk-Strang splitting technique and involves
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Optimal transport for mesh adaptivity and shock capturing of compressible flows J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-16 Ngoc Cuong Nguyen, R. Loek Van Heyningen, Jordi Vila-Pérez, Jaime Peraire
We present an optimal transport approach for mesh adaptivity and shock capturing of compressible flows. Shock capturing is based on a viscosity regularization of the governing equations by introducing an artificial viscosity field as solution of the modified Helmholtz equation. Mesh adaptation is based on the optimal transport theory by formulating a mesh mapping as solution of Monge-Ampère equation
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Regularized Stokeslet surfaces J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-16 Dana Ferranti, Ricardo Cortez
A variation of the Method of Regularized Stokeslets (MRS) in three dimensions is developed for triangulated surfaces with a piecewise linear force density. The work extends the regularized Stokeslet segment methodology used for piecewise linear curves. By using analytic integration of the regularized Stokeslet kernel over the triangles, the regularization parameter is effectively decoupled from the
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A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-16 Atul Agrawal, Phaedon-Stelios Koutsourelakis
We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. The proposed closure consists of two parts. A parametric one, which utilizes previously proposed, neural-network-based tensor basis functions dependent on the rate of strain and rotation tensor invariants. This is complemented by latent, random variables which
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An entropy conserving/stable discontinuous Galerkin solver in entropy variables based on the direct enforcement of entropy balance J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-15 Luca Alberti, Emanuele Carnevali, Alessandro Colombo, Andrea Crivellini
Numerical schemes that guarantee the preservation of flow properties as prescribed by physical laws, ensure high-fidelity results and improved computational robustness. This work presents a highly accurate entropy conserving/stable solver for the solution of the compressible Euler equations. The method uses a modal Discontinuous Galerkin approximation and takes advantage of both entropy variables and
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Energy-conserving neural network for turbulence closure modeling J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-10 T. van Gastelen, W. Edeling, B. Sanderse
In turbulence modeling, we are concerned with finding closure models that represent the effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards machine learning techniques to construct such models. However, the stability of machine-learned closure models and their abidance by physical structure (e.g. symmetries, conservation laws) are still open problems. To tackle
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Numerical optimization of Neumann eigenvalues of domains in the sphere J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-10 Eloi Martinet
This paper deals with the numerical optimization of the first three eigenvalues of the Laplace-Beltrami operator of domains in the Euclidean sphere of with Neumann boundary conditions. We address two approaches: the first one is a generalization of the initial problem leading to a density method and the other one is a shape optimization procedure using the level-set method. The original goal of those
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A new type of modified MR-WENO schemes with new troubled cell indicators for solving hyperbolic conservation laws in multi-dimensions J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-10 Huimin Zuo, Jun Zhu
In this paper, a new type of increasingly high-order modified multi-resolution weighted essentially non-oscillatory (MMR-WENO) schemes with new troubled cell indicators is designed in the finite difference framework for solving hyperbolic conservation laws in one, two, and three dimensions. It is a first time to design new troubled cell indicators that based on two high-degree reconstruction polynomials
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SPRAY: A smoothed particle radiation hydrodynamics code for modeling high intensity laser-plasma interactions J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-09 Min Ki Jung, Hakhyeon Kim, Su-San Park, Eung Soo Kim, Yong-Su Na, Sang June Hahn
Here we report the development of SPRAY, a massively parallel GPU accelerated, smoothed particle hydrodynamics (SPH)-based, radiation hydrodynamics (RHD) code designed specifically for simulating high intensity laser-plasma interactions. When a target is irradiated by an intense laser, highly complex fluid deformation occurs due to instabilities, which is challenging to study numerically. SPRAY is
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Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-08 Guosheng Fu, Stanley Osher, Will Pazner, Wuchen Li
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we first apply high-order finite element methods to discretize the space-time domain and then solve the optimal control problem using augmented Lagrangian methods (ALG2)
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Positional embeddings for solving PDEs with evolutional deep neural networks J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-08 Mariella Kast, Jan S. Hesthaven
This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time-dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on eigenfunctions of the Laplace-Beltrami operator, geometric properties are encoded intrinsically and Dirichlet, Neumann and periodic boundary conditions of the PDE solution
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Learning stochastic dynamical system via flow map operator J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-08 Yuan Chen, Dongbin Xiu
We present a numerical framework for learning unknown stochastic dynamical systems using measurement data. Termed stochastic flow map learning (sFML), the new framework is an extension of flow map learning (FML) that was developed for learning deterministic dynamical systems. For learning stochastic systems, we define a stochastic flow map that is a superposition of two sub-flow maps: a deterministic
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A high-order diffused-interface approach for two-phase compressible flow simulations using a discontinuous Galerkin framework J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-08 Niccolò Tonicello, Matthias Ihme
A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and sharpening terms in the phase field equation, where the former term involves the computation of the local interface normal vectors. Due to the well-known Gibbs phenomenon
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A general positivity-preserving algorithm for implicit high-order finite volume schemes solving the Euler and Navier-Stokes equations J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-06 Qian-Min Huang, Hanyu Zhou, Yu-Xin Ren, Qian Wang
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Semi-discrete entropy-preserving surface reconstruction schemes for the shallow water equations: Analysis of physical structures J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-06 Jian Dong, Xu Qian
We aim to introduce a new variant of hydrostatic reconstruction scheme, which is physical-structure-preserving and semi-discrete entropy-preserving for shallow water equations with a discontinuous bottom topography, based on novel surface reconstructions (NSR). The NSR is used to define approximate Riemann states with respect to the water depth and the velocity to compute consistent numerical fluxes
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Unified approach to artificial compressibility and local low Mach number preconditioning J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-05 Minsoo Kim, Seungsoo Lee
This paper presents a unified approach to artificial compressibility and local low Mach number preconditioning methods. The numerical formulation is presented, which provides a seamless transition between incompressible and compressible systems. A single preconditioner that can act as the artificial compressibility or the local preconditioning under a given Mach number condition is derived. An artificial
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A Cartesian mesh approach to embedded interface problems using the virtual element method J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-05 M. Arrutselvi, Sundararajan Natarajan
In this paper, we propose an elegant methodology to treat sharp interfaces that are implicitly defined which does not require (a) enrichment functions, (b) additional linear and bilinear terms such as the inter-element penalty terms as in Nitsche's method, or use of multipliers like Lagrange multiplier, in the weak form for enforcing the jump conditions across the interface, and (c) modification to
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Spatial second-order positive and asymptotic preserving filtered PN schemes for nonlinear radiative transfer equations J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-05 Xiaojing Xu, Song Jiang, Wenjun Sun
A spatial second-order scheme for the nonlinear radiative transfer equations is introduced in this paper. The discretization scheme is based on the filtered spherical harmonics () method for the angular variable and the unified gas kinetic scheme (UGKS) framework for the spatial and temporal variables respectively. In order to keep the scheme positive and second-order accuracy, firstly, we use the
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A non-oscillatory finite volume scheme using a weighted smoothed reconstruction J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-03 Davoud Mirzaei, Navid Soodbakhsh
In this research article, we introduce a high-order and non-oscillatory finite volume method in combination with radial basis function approximations and use it for the solution of scalar conservation laws on unstructured meshes. This novel approach departs from conventional non-oscillatory techniques, which often require the use of multiple stencils to achieve smooth reconstructions. Instead, the
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Efficient particle control in systems with large density gradients J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-03 Evan K. Massaro, Michael A. Gallis, Nicolas G. Hadjiconstantinou
Simulations of large density gradients present a number of challenges for direct Monte Carlo methods, since they lead to too few particles in dilute regions and prohibitively many in the dense regions. We propose a particle control methodology that gives the user more control of the number of particles per cell by introducing a variable weight for each particle. The proposed scheme is based on the
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A high-order finite difference method for moving immersed domain boundaries and material interfaces J. Comput. Phys. (IF 4.1) Pub Date : 2024-04-02 James Gabbard, Wim M. van Rees
We present a high-order sharp treatment of immersed moving domain boundaries and material interfaces, and apply it to the advection-diffusion equation in two and three dimensions. The spatial discretization combines dimension-split finite difference schemes with an immersed boundary treatment based on a weighted least-squares reconstruction of the solution, providing stable discretizations with up
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Decoding mean field games from population and environment observations by Gaussian processes J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-29 Jinyan Guo, Chenchen Mou, Xianjin Yang, Chao Zhou
This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover agents' strategic actions and the environment's configurations from partial and noisy observations of the population of agents and the setup of the environment. Our
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Data-driven models of nonautonomous systems J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-29 Hannah Lu, Daniel M. Tartakovsky
Nonautonomous dynamical systems are characterized by time-dependent inputs, which complicates the discovery of predictive models describing the spatiotemporal evolution of the state variables of quantities of interest from their temporal snapshots. When dynamic mode decomposition (DMD) is used to infer a linear model, this difficulty manifests itself in the need to approximate the time-dependent Koopman
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An efficient unconditional energy stable scheme for the simulation of droplet formation J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-29 Jinpeng Zhang, Changjuan Zhang, Xiaoping Wang
We have developed an efficient and unconditionally energy-stable method for simulating droplet formation dynamics. Our approach involves a novel time-marching scheme based on the scalar auxiliary variable technique, specifically designed for solving the Cahn-Hilliard-Navier-Stokes phase field model with variable density and viscosity. We have successfully applied this method to simulate droplet formation
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Learning nonparametric ordinary differential equations from noisy data J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-29 Kamel Lahouel, Michael Wells, Victor Rielly, Ethan Lew, David Lovitz, Bruno M. Jedynak
Learning nonparametric systems of Ordinary Differential Equations (ODEs) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for for which the solution of the ODE exists and is unique. Learning consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively
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DOT-type schemes for hybrid hyperbolic problems arising from free-surface, mobile-bed, shallow-flow models J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-28 Daniel Zugliani, Giorgio Rosatti
Free-surface, mobile-bed, shallow-flow models may present Hybrid hyperbolic systems of partial differential equations characterised by conservative and non-conservative fluxes that can only be expressed in primitive variables. This paper presents the effort we made to derive DOT-type schemes (Osher-type schemes derived by Dumbser and Toro, 2011 ) for these kinds of systems formulated for the one-dimensional
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A MCMC method based on surrogate model and Gaussian process parameterization for infinite Bayesian PDE inversion J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-28 Zheng Hu, Hongqiao Wang, Qingping Zhou
This work focuses on an inversion problem derived from parametric partial differential equations (PDEs) with an infinite-dimensional parameter, represented as a coefficient function. The objective is to estimate this coefficient function accurately despite having only noisy measurements of the PDE solution at sparse input points. Conventional methods for inversion require numerous calls to a refined
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Information theoretic clustering for coarse-grained modeling of non-equilibrium gas dynamics J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-28 Christian Jacobsen, Ivan Zanardi, Sahil Bhola, Karthik Duraisamy, Marco Panesi
We present a new framework towards the objective of learning coarse-grained models based on the maximum entropy principle. We show that existing methods for assigning clusters using the maximum entropy approach are heuristic or sub-optimal. We propose a machine learning framework informed by rate-distortion theory to learn optimal cluster assignments, aiming to improve the effectiveness of the coarse-graining
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Meshless interface tracking for the simulation of dendrite envelope growth J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-28 Mitja Jančič, Miha Založnik, Gregor Kosec
The growth of dendritic grains during solidification is often modelled using the Grain Envelope Model (GEM), in which the envelope of the dendrite is an interface tracked by the Phase Field Interface Capturing (PFIC) method. In the PFIC method, an phase-field equation is solved on a fixed mesh to track the position of the envelope. While being versatile and robust, PFIC introduces certain numerical
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Spectrally-tuned compact finite-difference schemes with domain decomposition and applications to numerical relativity J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-27 Boris Daszuta
Compact finite-difference (FD) schemes specify derivative approximations implicitly, thus to achieve parallelism with domain-decomposition suitable partitioning of linear systems is required. Consistent order of accuracy, dispersion, and dissipation is crucial to maintain in wave propagation problems such that deformation of the associated spectra of the discretized problems is not too severe. In this
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A robust phase-field method for two-phase flows on unstructured grids J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-27 Hanul Hwang, Suhas S. Jain
A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to local grid size. In addition to this, we present a novel formulation for two-phase flows on collocated grids that is provably energy stable, which is a critical feature
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A hybrid finite difference level set–implicit mesh discontinuous Galerkin method for multi-layer coating flows J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-27 Luke P. Corcos, Robert I. Saye, James A. Sethian
A mathematical model and numerical framework are presented for computing multi-physics multi-layer coating flow dynamics, with applications to the leveling of multi-layer paint films. The algorithm combines finite difference level set methods and high-order accurate sharp-interface implicit mesh discontinuous Galerkin methods to capture a complex set of multi-physics, incorporating Marangoni-driven
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Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-27 Nabil M. Atallah, Vladimir Z. Tomov, Guglielmo Scovazzi
We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces
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Multicomponent droplet evaporation in a geometric volume-of-fluid framework J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-26 Edoardo Cipriano, Abd Essamade Saufi, Alessio Frassoldati, Tiziano Faravelli, Stéphane Popinet, Alberto Cuoci
This work proposes an innovative model for multicomponent phase change in interface-resolved simulations. The two-phase system is described by a geometric Volume-Of-Fluid (VOF) approach, and considers multiple components in non-isothermal environments, relaxing the hypothesis of pure liquid droplets usually studied in the literature. The model includes the Stefan flow and implements the following solutions
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Scalable implicit solvers with dynamic mesh adaptation for a relativistic drift-kinetic Fokker–Planck–Boltzmann model J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-26 Johann Rudi, Max Heldman, Emil M. Constantinescu, Qi Tang, Xian-Zhu Tang
In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. We develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management
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A geometrically and thermodynamically compatible finite volume scheme for continuum mechanics on unstructured polygonal meshes J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-25 Walter Boscheri, Raphaël Loubère, Jean-Philippe Braeunig, Pierre-Henri Maire
We present a novel Finite Volume (FV) scheme on unstructured polygonal meshes that is provably compliant with the Second Law of Thermodynamics and the Geometric Conservation Law (GCL) at the same time. The governing equations are provided by a subset of the class of symmetric and hyperbolic thermodynamically compatible (SHTC) models introduced by Godunov in 1961. Specifically, our numerical method
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A multi-fidelity transfer learning strategy based on multi-channel fusion J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-25 ZiHan Zhang, Qian Ye, DeJin Yang, Na Wang, GuoXiang Meng
Multi-fidelity strategies leverage a large amount of low-fidelity data combined with a smaller set of high-fidelity data, thereby achieving satisfactory results at a reasonable cost. In our research, we introduce an innovative multi-fidelity strategy that integrates the concepts of multi-fidelity data fusion and transfer learning. In the proposed framework, we incorporate auto-encoders and a multi-channel
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Latent assimilation with implicit neural representations for unknown dynamics J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-22 Zhuoyuan Li, Bin Dong, Pingwen Zhang
Data assimilation is crucial in a wide range of applications, but it often faces challenges such as high computational costs due to data dimensionality and incomplete understanding of underlying mechanisms. To address these challenges, this study presents a novel assimilation framework, termed Latent Assimilation with Implicit Neural Representations (LAINR). By introducing Spherical Implicit Neural
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Uncertainty quantification in autoencoders predictions: Applications in aerodynamics J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-22 Ettore Saetta, Renato Tognaccini, Gianluca Iaccarino
A data-driven model is compared to classical equation-driven approaches to investigate its ability to predict quantity of interest and their uncertainty when studying airfoil aerodynamics. The focus is on autoencoders and the effect of uncertainties due to the architecture, the hyperparamaters and the choice of the training data (internal or model-form uncertainties). Comparisons with a Gaussian Process
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Weak-PDE-LEARN: A weak form based approach to discovering PDEs from noisy, limited data J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-21 Robert Stephany, Christopher Earls
We introduce , a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. uses an adaptive loss function based on weak forms to train a neural network, , to approximate the PDE solution while simultaneously identifying the governing PDE. This approach yields an algorithm that is robust to noise and can discover a
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Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-20 Di Zhou, H. Jane Bae
In this study, we conduct a parametric analysis to evaluate the sensitivities of wall-modeled large-eddy simulation (LES) with respect to subgrid-scale (SGS) models, mesh resolution, wall boundary conditions and mesh anisotropy. While such investigations have been conducted for attached/flat-plate flow configurations, systematic studies specifically targeting turbulent flows with separation are notably
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A novel surface-derivative-free of jumps AIIM with triangulated surfaces for 3D Helmholtz interface problems J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-20 Zhijun Tan, Jianjun Chen, Weiyi Wang
Triangular surface-based 3D IIM (Immersed Interface Method) algorithms face major challenges due to the need to calculate surface derivative of jumps. This paper proposes a fast, easy-to-implement, surface-derivative-free of jumps, augmented IIM (AIIM) with triangulated surfaces for 3D Helmholtz interface problems for the first time, which combines the simplified AIIM with domain decomposed and embedding
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Efficient quadratures for high-dimensional Bayesian data assimilation J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-20 Ming Cheng, Peng Wang, Daniel M. Tartakovsky
Bayesian update is a common strategy used to combine (uncertain) model predictions and (noisy) observational data. A computational bottleneck in this data assimilation technique is the evaluation of high-dimensional quadratures involving multivariate probability density functions (PDFs) of system states. We explore “designed quadratures” as a means to reduce the computational cost of Bayesian update
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Mitigating spectral bias for the multiscale operator learning J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-19 Xinliang Liu, Bo Xu, Shuhao Cao, Lei Zhang
Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important applications such as reservoir modeling and turbulence prediction. We demonstrate that for such PDEs, the spectral bias towards low-frequency components presents a
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Tensor networks for solving the time-independent Boltzmann neutron transport equation J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-19 Duc P. Truong, Mario I. Ortega, Ismael Boureima, Gianmarco Manzini, Kim Ø. Rasmussen, Boian S. Alexandrov
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial Differential Equations (PDEs). Here, we present a mixed Tensor Train (TT)/Quantized Tensor Train (QTT) approach for the numerical solution of time-independent Boltzmann
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Monte Carlo on manifolds in high dimensions J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-19 Kerun Xu, Miranda Holmes-Cerfon
We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018) ), where the manifold is defined by the level set of constraint functions, and the probability distribution may involve the pseudodeterminant of the Jacobian of the constraints, as arises in physical
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Low-rank Monte Carlo for Smoluchowski-class equations J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-18 A.I. Osinsky
The work discusses a new low-rank Monte Carlo technique to solve Smoluchowski-like kinetic equations. It drastically decreases the computational complexity of modeling of size-polydisperse systems. For the studied systems it can outperform the existing methods by more than ten times; its superiority further grows with increasing system size. Application to the recently developed temperature-dependent
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A metric-based adaptive mesh refinement criterion under constrain for solving elliptic problems on quad/octree grids J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-18 Lucas Prouvost, Anca Belme, Daniel Fuster
In this work we propose and investigate the performance of a metric-based refinement criteria for adaptive meshing used for improving the numerical solution of an elliptic problem. We show that in general, when solving elliptic equations such as the Poisson-Helmholtz equation, the minimization of the interpolation error often used as local refinement criteria does not always guarantee the minimization
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A stochastic Fokker–Planck–Master model for diatomic rarefied gas flows J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-18 Sanghun Kim, Eunji Jun
The direct simulation Monte Carlo (DSMC) method is widely used for numerical solutions of the Boltzmann equation. However, the associated computational cost becomes prohibitive in the near-continuum regime. To address this limitation, the particle-based Fokker–Planck (FP) method has been extensively studied in the past decade. The FP equation, which describes Brownian motion, does not require resolution
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High-order finite volume multi-resolution WENO schemes with adaptive linear weights on triangular meshes J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-18 Yicheng Lin, Jun Zhu
This paper presents high-order finite volume multi-resolution weighted essentially non-oscillatory schemes with adaptive linear weights to solve hyperbolic conservation laws on triangular meshes. They are abbreviated as the ALW-MR-WENO schemes. The novel third-order, fourth-order, and fifth-order ALW-MR-WENO schemes are designed by applying two unequal-sized hierarchical central stencils in comparison
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History of CFD Part II: The poster J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-16 Bram van Leer
The genesis and contents of the 2010 poster "History of CFD Part II" are described.
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An adaptive phase-field method for structural topology optimization J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-16 Bangti Jin, Jing Li, Yifeng Xu, Shengfeng Zhu
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive procedure is driven by two residual type a posteriori error estimators, one for the state variable and the other for the first-order optimality condition of the objective
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An adaptive low-rank splitting approach for the extended Fisher–Kolmogorov equation J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-16 Yong-Liang Zhao, Xian-Ming Gu
The extended Fisher–Kolmogorov (EFK) equation has been used to describe some phenomena in physical, material and biological systems. In this paper, we propose a full-rank splitting scheme and a rank-adaptive splitting approach for this equation. We first use a finite difference method to approximate the space derivatives. Then, the resulting semi-discrete system is split into two stiff linear parts
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DynAMO: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-16 T. Dzanic, K. Mittal, D. Kim, J. Yang, S. Petrides, B. Keith, R. Anderson
We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide
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A model reduction method for parametric dynamical systems defined on complex geometries J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-16 Huailing Song, Yuming Ba, Dongqin Chen, Qiuqi Li
Dynamic mode decomposition (DMD) describes the dynamical system in an equation-free manner and can be used for the prediction and control. It is an efficient data-driven method for the complex systems. In this paper, we extend DMD to the parameterized problems and propose a model reduction method based on DMD to improve the computation efficiency. This method is an offline-online mechanism. In the
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Fluid-reduced-solid interaction (FrSI): Physics- and projection-based model reduction for cardiovascular applications J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-16 Marc Hirschvogel, Maximilian Balmus, Mia Bonini, David Nordsletten
Fluid-solid interaction (FSI) phenomena play an important role in many biomedical engineering applications. While FSI techniques and models have enabled detailed computational simulations of flow and tissue motion, the application of FSI can present challenges, particularly when data for constraining models is sparse and/or when fast computational simulations are required for assessment. In this paper
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A cluster analysis-based shock wave pattern recognition method for two-dimensional inviscid compressible flows J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-15 Siyuan Chang, Jun Liu, Kai Cui
Compressible flows typically exhibit multiple shock waves which interact with each other, making the detection of these shock waves crucial for various aspects of flow studies including construction of high-order numerical schemes (e.g., shock-fitting), adaptive grid refinement, and flow visualization. This study aims to effectively identify and localize multiple shock waves and their interaction points
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Computing multi-eigenpairs of high-dimensional eigenvalue problems using tensor neural networks J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-15 Yifan Wang, Hehu Xie
In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding eigenfunctions is one of the basic tasks in mathematical and computational physics. With the help of tensor neural network, the high dimensional integrations included
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Physics-informed polynomial chaos expansions J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-15 Lukáš Novák, Himanshu Sharma, Michael D. Shields
Developing surrogate models for costly mathematical models representing physical systems is challenging since it is typically not possible to generate large training data sets, i.e. to create a large experimental design. In such cases, it can be beneficial to constrain the surrogate approximation to adhere to the known physics of the model. This paper presents a novel methodology for the construction
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The generalized Riemann problem scheme for a laminar two-phase flow model with two-velocities J. Comput. Phys. (IF 4.1) Pub Date : 2024-03-15 Qinglong Zhang, Wancheng Sheng
In this paper, we propose a generalized Riemann problem (GRP) scheme for a laminar two-phase flow model. The model takes into account the distinctions between different densities and velocities, and is obtained by averaging vertical velocities across each layer for the two-phase flows. The rarefaction wave and the shock wave are analytically resolved by using the Riemann invariants and Rankine-Hugoniot