Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. In this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous

Coupling of a 2D model and a 1D model, to form a hybrid mixed-dimensional model, is considered in the context of elastic wave propagation. A Dirichlet-to-Neumann (DtN) method is used to perform this coupling. This approach is an extension of previous work (which was applied to steady-state wave problems) to the time-dependent regime. It is based on enforcing the continuity of the DtN map, relating

Previous work has introduced the stability analysis of coupled neutronics-depletion solvers for the standard explicit Euler and predictor-corrector methods. The present work is an extension of this analysis to higher-order schemes that are commonly used, including the LE, LE/LI, LE/QI, and their implicit versions where such a method exists. Substepping, extrapolation, and linear and quadratic interpolation

We develop a fluid–structure interaction numerical algorithm based on the immersed boundary (IB) method for simulating the interaction between air–water two-phase flows and thin flexible structures. In this algorithm, we propose a new method to avoid the unphysical fluxes across the thin structures, which effectively mitigates the issue of flow spurious penetration. In the proposed method, an explicit

In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the resulting multiscale dynamics are challenging to resolve numerically. Using conventional computational fluid dynamics (CFD) requires excessive computing cost. Here

The scalar auxiliary variable (SAV) approach [42] is a very popular and efficient method to simulate various phase field models. To save the computational cost, a new SAV approach is given in [25] by introducing a new variable θ. The new SAV approach can be proved to save nearly half CPU time of the original SAV approach while keeping all its other advantages. In this paper, we propose a novel technique

We present a numerical method to obtain self-similar solutions of the ideal magnetohydrodynamics (MHD) equations. Under a self-similar transformation, the initial value problem (IVP) is converted into a boundary value problem (BVP) by eliminating time and transforming the system to self-similar coordinates (ξ≡x/t,η≡y/t). The ideal MHD system of equations is augmented by a generalized Lagrange multiplier

We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the solution, and we establish their energy stability. This class includes as a special case high order, unconditionally stable schemes obtained via convexity splitting

A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities

In the last decade, there has been a lot of interest in developing high-order methods as viable option for unsteady scale-resolving-simulations which are increasingly important in the industrial design process. High-order methods offer the advantage of low numerical dissipation, high efficiency on modern architectures and quasi mesh-independence. Despite significant advances in high-order solution

A reduced model for large deformations of prestrained plates consists of minimizing a second order bending energy subject to a nonconvex metric constraint. The former involves the second fundamental form of the middle plate and the latter is a restriction on its first fundamental form. We discuss a formal derivation of this reduced model along with an equivalent formulation that makes it amenable computationally

A novel, simple, robust, and effective modification in the nonlinear weights of the scale-invariant WENO operator is proposed that achieves an optimal order of accuracy with smooth function regardless of the critical point (Cp-property), a scale-invariant with an arbitrary scaling of a function (Si-property), an essentially non-oscillatory approximation of a discontinuous function (ENO-property), and

Flow in fractured porous media is of high relevance in a variety of geotechnical applications, given the fact that they ubiquitously occur in nature and that they can have a substantial impact on the hydraulic properties of rock. As a response to this, an active field of research has developed over the past decades, focussing on the development of mathematical models and numerical methods to describe

The immersed boundary method (IBM) of Peskin (J. Comput. Phys., 1977), and derived forms such as the projection method of Taira and Colonius (J. Comput. Phys., 2007), have been useful for simulating flow physics in problems with moving interfaces on stationary grids. However, in their interface treatment, these methods do not distinguish one side from the other, but rather, apply the motion constraint

We introduce a robust and high order strategy to perform the reinitialization in a level set framework. The reinitialization by closest points (RCP) method is based on geometric considerations. It relies on a gradient descent to find the closest points at the interface in order to solve the Eikonal equation and thus reinitializing the level set field. Furthermore, a new algorithm, also based on a similar

Despite their well-known limitations, Reynolds averaged Navier-Stokes (RANS) models remain the most commonly employed tool for modeling turbulent flows in engineering practice. RANS models are predicated on the solution of the RANS equations, but the RANS equations involve an unclosed term, the Reynolds stress tensor, which must be modeled. The Reynolds stress tensor is often modeled as an algebraic

Sketching is a stochastic dimension reduction method that preserves geometric structures of data and has applications in high-dimensional regression, low rank approximation and graph sparsification. In this work, we show that sketching can be used to compress simulation data and still accurately estimate time autocorrelation and power spectral density. For a given compression ratio, the accuracy is

In many applications, it is impractical—if not even impossible—to obtain data to fit a known cubature formula (CF). Instead, experimental data is often acquired at equidistant or even scattered locations. In this work, stable (in the sense of nonnegative only cubature weights) high-order CFs are developed for this purpose. These are based on the approach to allow the number of data points N to be larger

Entropy stable schemes replicate an entropy inequality at the semi-discrete level. These schemes rely on an algebraic summation-by-parts (SBP) structure and a technique referred to as flux differencing. We provide simple and efficient formulas for Jacobian matrices for the semi-discrete systems of ODEs produced by entropy stable discretizations. These formulas are derived based on the structure of

In this work we present a novel exact Riemann solver for an artificial Equation of State (EoS) based modification of the incompressible Euler equations. Differently from the well known artificial compressibility method, this new approach overcomes the lack of the pressure-velocity coupling by using a suitably designed artificial EoS. The modified set of equations fits into the framework of first order

A new sub-grid-scale model is developed for studying influences of the Hall term on macroscopic aspects of magnetohydrodynamic turbulence. Although the Hall term makes numerical simulations extremely expensive by exciting high-wave-number coefficients and makes magnetohydrodynamic equations stiff, studying macroscopic aspects of magnetohydrodynamic turbulence together with the Hall term is meaningful

A dynamic mode decomposition (DMD) based reduced-order model (ROM) is developed for tracking, detection, and prediction of kinetic plasma behavior. DMD is applied to the high-fidelity kinetic plasma model based on the electromagnetic particle-in-cell (EMPIC) algorithm to extract the underlying dynamics and key features of the model. In particular, the ability of DMD to reconstruct the spatial pattern

We develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation

The Boltzmann equation with the Bhatnagar-Gross-Krook collision model (Boltzmann-BGK equation) has been widely employed to describe multiscale flows, i.e., from the hydrodynamic limit to free molecular flow. In this study, we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum

Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based -optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that evolves proportionally to the transported flux. In this paper we present an extension of this model that considers a time derivative of the conductivity that grows as

The time-dependent, gray, linear radiation transport equation is discretized using the meshless local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only depends on the position and extent of the kernels. The resolution of the integration automatically follows the particles and requires no manual adjustment

In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out on structured rectangular mesh. For both schemes, the fifth-order WENO-AO reconstruction is adopted to achieve a high-order spatial accuracy. In terms of temporal discretization, a two-stage fourth-order (S2O4) time marching strategy is adopted

In this paper, the WLS-ENO (Weighted-Least-Squares based Essentially Non-Oscillatory) reconstruction is modified to maintain the conservation of the cell average values. Furthermore, the divergence-free constraint is combined with the conservative WLS-ENO reconstruction, which can make the magnetic field locally divergence-free. The main merit of the proposed reconstruction scheme is that it can keep

The Green's functions for the Laplace equation satisfying the Dirichlet and Neumann boundary conditions on the upper side of the infinite plane with a circular hole are introduced and studied. These functions enable solutions of the boundary value problems in domains where the hole is closed by an arbitrary mesh (locally rough surfaces). The developed approach accounts for arbitrary positive and negative

It is challenging to solve the Boltzmann equation accurately due to the extremely high dimensionality and nonlinearity. This paper addresses the idea and implementation of the first flux reconstruction method for high-order Boltzmann solutions. Based on the Lagrange interpolation and reconstruction, the kinetic upwind flux functions are solved simultaneously within physical and particle velocity space

In this paper, a compact fifth-order gas-kinetic scheme (GKS) is proposed to solve the Euler equations of compressible flows. It is based on the framework of a one-stage efficient high-order GKS (EHGKS), which can achieve arbitrary high-order accuracy in both space and time, and the newly-developed compact reconstruction technique, combining both the ideas of the simple weighted essentially non-oscillatory

Adaptivity is crucial for addressing practical challenges of the next decades. In this regard, recent surveys [117] highlight that it continues to be a major bottleneck in computational fluid dynamics workflow. We introduce mixed non-conforming discontinuous Galerkin discretization for the full Boltzmann equation in 2D/3D. These schemes have been designed for efficiency — motivated in part by spectral

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian processes. The proposed approach: (1) provides a natural generalization of collocation kernel methods to nonlinear PDEs and IPs; (2) has guaranteed convergence for

The study of cold plasma represents a very active field of applied physics with technical applications ranging from medical treatments to estimation of aging of electrical components due to internal partial discharges and treeing. In particular, the simulation of this category of plasma plays an increasingly important role since more and more complex, and technically relevant, configurations can be

The paper presents an extended and advanced boundary integral equation method (BIEM) for simulating the elastic wave excitation and propagation in a layered piezoelectric phononic crystal with a strip-like crack or electrode. The method is based on the integral representation in terms of the Fourier transform of the Green's matrix for the whole piezoelectric laminate. A novel algorithm for constructing

The present study proposes an accurate lattice Boltzmann direct coupling algorithm, well suited for industrial purposes, making it highly valuable for aeroacoustic applications. It is indeed known that the convection of vortical structures across a grid refinement interface, where cell size is abruptly doubled, is likely to generate spurious noise that may corrupt the solution over the whole computational

An original spectral study of the compressible hybrid lattice Boltzmann method (HLBM) on standard lattice is proposed. In this framework, the mass and momentum equations are addressed using the lattice Boltzmann method (LBM), while finite difference (FD) schemes solve an energy equation. Both systems are coupled with each other thanks to an ideal gas equation of state. This work aims at answering some

In this work, an elastic-perfectly plastic model in two-dimensional planar geometry is studied and a new HLLC-type approximate Riemann solver (HLLCN) is put forward. The main feature of the new approximate Riemann solver is that it almost includes all stress waves, such as elastic, plastic, longitudinal and shear waves simultaneously in the presence of elastic-plastic phase transition. The analyses

In this paper, we design a new type of high order weighted compact scheme based on ZJS method (Zhang et al., 2008) [35] and ZQ method (Zhu and Qiu, 2016) [16]. These nonlinear weighted compact schemes are designed based on the cell-centered compact scheme of Lele (Lele, 1992) [22]. Instead of using WENO interpolation with equal-sized sub-stencil in ZJS formulae in Zhang et al. (2008) [35] for the fluxes

A reduced basis method based on a physics-informed machine learning framework is developed for efficient reduced-order modeling of parametrized partial differential equations (PDEs). A feedforward neural network is used to approximate the mapping from the time-parameter to the reduced coefficients. During the offline stage, the network is trained by minimizing the weighted sum of the residual loss

We present a proof by analysis and numerical results that Van Leer's MUSCL conservative scheme with the discretization parameter κ is third-order accurate for κ=1/3. We include both the original finite-volume MUSCL family, updating cell-averaged values of the solution, and the related finite-difference version, updating point values. The presentation is needed because in the CFD literature claims have

Modeling chemical reactions on the basis of probabilistic rules has been employed in Lagrangian schemes to simulate transport of solutes in porous media. Reactive random walk particle tracking allows reagents particle pairs to interact proportionally to their separation distance and the nature of the chemical process. However, most of the available algorithms result to be computationally prohibitive

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in the optimisation as apposed to making them part of the loss function. The resulting models are discretised in space by the finite element method (FEM). The method

The diffusion and bootstrap percolation models were studied in regular random and Erdős-Rényi networks using the modified Newman-Ziff algorithms. We calculated the percolation threshold and the order parameter of the percolation transition (strength of the giant cluster) and its derivatives. The percolation transitions are classified by the results. The diffusion percolation with a small k has a double

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing equations are not known as a prior. In addition, significant measurement noise and complex algorithm hyperparameter tuning usually reduces the robustness of existing

We present an effective asymptotic Green's function method for propagating the waves through the linear scalar wave equation. The wave is first split into its forward-propagating and backward-propagating parts. Following that, the method, which combines the Huygens' principle and the geometrical optics approximations, is designed to propagate the forward-propagating and backward-propagating waves,

This paper introduces a factorization for the inverse of discrete Fourier integral operators of size N×N that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a hierarchical matrix representation is constructed for the hermitian matrix arising from composing the Fourier integral operator with its adjoint. This representation

Space plasma simulations have seen an increase in the use of magnetohydrodynamic (MHD) with embedded Particle-in-Cell (PIC) models. This combined MHD-EPIC algorithm simulates some regions of interest using the kinetic PIC method while employing the MHD description in the rest of the domain. The MHD models are highly efficient and their fluid descriptions are valid for most part of the computational

In this paper, a deep learning method using Koopman operator is presented for modeling nonlinear multiscale dynamical problems. Koopman operator is able to transform a non- linear dynamical system into a linear system in a Koopman invariant subspace. However, it is usually very challenging to choose a set of suitable observation functions spanning the Koopman invariant subspace when only data is available

Volume of fluid(VOF) method is a sharp interface method employed for simulations of two phase flows. Interface in VOF is usually represented using piecewise linear line segments in each computational grid based on the volume fraction field. While VOF for cartesian coordinates conserve mass exactly, existing algorithms do not show machine-precision mass conservation for axisymmetric coordinate systems

In this paper, a new type of high-order finite volume and finite difference multi-resolution Hermite weighted essentially non-oscillatory (HWENO) schemes are designed for solving hyperbolic conservation laws on structured meshes. Here we only use the information defined on a hierarchy of nested central spatial stencils but do not introduce any equivalent multi-resolution representation, the terminology

In this paper, we present a fully implicit mimetic finite difference method (MFD) for general fractured reservoir simulation. The MFD is a novel numerical discretization scheme that has been successfully applied to many fields and it is characterized by local conservation properties and applicability to complex grids. In our work, we extend this method to the numerical simulation of fractured reservoirs

Fractional Ginzburg-Landau equations as generalizations of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integration method for space fractional Ginzburg-Landau equations based on a dynamical low-rank approximation. We first approximate the space fractional derivatives by using a fractional centered difference method. Then, the resulting

WENO schemes are a popular class of shock-capturing schemes which adopt an adaptive-stencil approach to interpolation. WENO schemes rely on smoothness indicators to assess the relative smoothness of the solution within the sub-stencils. Computing these smoothness indicators is the most expensive operation in the WENO reconstruction procedure. In this paper, an efficient algorithm is proposed to compute

We present a k-exact reconstruction method, which can be incorporated into vertex-centered unstructured finite-volume flow solvers to maintain a high-order accurate solution in space. The scheme is combined with a fractional step strategy for the solution of the incompressible Navier-Stokes equations with a fully implicit discretization of a Poisson equation for the pressure correction. This also involves

This paper discusses a new class of optimized implicit-explicit Runge-Kutta methods for the numerical solution of the dispersive and non-dispersive hyperbolic systems. Optimized implicit-explicit methods are formulated for the better stability and dispersion properties. Moreover, for present methods inversion of the coefficient matrices is not necessary, which makes these methods very attractive in

We propose an energy-stable parametric finite element method (ES-PFEM) to discretize the motion of a closed curve under surface diffusion with an anisotropic surface energy γ(θ) – anisotropic surface diffusion – in two dimensions, while θ is the angle between the outward unit normal vector and the vertical axis. By introducing a positive definite surface energy (density) matrix G(θ), we present a new

With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation. This novel scheme can significantly reduce the computational cost while retaining the same accuracy as the original procedure. Our phase-field method is built on top

Filtering the passive scalar transport equation in the large-eddy simulation (LES) of turbulent transport gives rise to the closure term corresponding to the unresolved scalar flux. Understanding and respecting the statistical features of subgrid-scale (SGS) flux is a crucial point in robustness and predictability of the LES. In this work, we investigate the intrinsic nonlocal behavior of the SGS passive