We present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel

We propose two new strategies based on Machine Learning techniques to handle polyhedral grid refinement, to be possibly employed within an adaptive framework. The first one employs the k-means clustering algorithm to partition the points of the polyhedron to be refined. This strategy is a variation of the well known Centroidal Voronoi Tessellation. The second one employs Convolutional Neural Networks

This paper presents an immersed boundary method for weak enforcement of Dirichlet boundary conditions on surfaces that are immersed in the stationary background discretizations. An interface stabilized form is developed by applying the Variational Multiscale Discontinuous Galerkin (VMDG) method at the immersed boundaries. The formulation is augmented with a variationally derived ghost-penalty type

In this work, we propose a novel phase-field model for the simulation of two-phase flows that is accurate, conservative, bounded, and robust. The proposed model conserves the mass of each of the phases, and results in bounded transport of the volume fraction. We present results from the canonical test cases of a drop advection and a drop in a shear flow, showing significant improvement in the accuracy

Dynamics of large-scale network processes underlies crucial phenomena ranging across all sciences. Forward simulation of large network models is often computationally prohibitive. Yet, most networks have intrinsic community structure. We exploit these communities and propose a fast simulation algorithm for network dynamics. In particular, aggregating the inputs a node receives constitutes the limiting

We present a new method for the geometric reconstruction of elastic surfaces simulated by the immersed boundary method with the goal of simulating the motion and interactions of cells in whole blood. Our method uses parameter-free radial basis functions for high-order meshless parametric reconstruction of point clouds and the elastic force computations required by the immersed boundary method. This

The wave structure of approximate Riemann solvers has a significant impact on the accuracy and computational requirements of finite volume codes. We propose a class of structurally complete approximate Riemann solvers (StARS) and provide an efficient means for analytically restoring the expansion wave to pre-existing three-wave solvers. The method analytically restores the expansion, is valid for arbitrary

We present a parametric reduced-order model for the neutral particle radiation transport equation. The approach devised is a minimally-intrusive, projection-based reduced-order model using global modes obtained via Proper Orthogonal Decomposition. The reduced-order model is specifically designed to work in a matrix-free fashion with radiation transport solvers relying on transport sweeps. The advantages

Here we propose hybrid Lagrangian–Eulerian (HLE) method for kinetic simulations of plasmas. The HLE method solves advection equations of shape functions unlike particle-in-cell (PIC) method. Although the PIC method cannot preserve the conservation laws of momentum and energy simultaneously, the HLE method can resolve this issue while the particle velocity is formulated by the Lagrangian description

We develop a controllability strategy for the computation of frequency-domain solutions of the 3D visco-elastic wave equation, in the perspective of seismic imaging applications. We generalize the controllability results for such equations beyond the sound-soft scattering (obstacle) problem. We detail the conjugate gradient implementation and show how an inner elliptic problem needs to be solved to

In this article, we present a novel RBF-WENO scheme improving the fifth-order WENO techniques for solving hyperbolic conservation laws. The numerical flux is implemented by incorporating radial basis function (RBF) interpolation to cell average data. To do this, the classical RBF interpolation is amended to be suitable for cell average data setting. With the aid of a locally fitting parameter in the

The thoracic diaphragm is the muscle that drives the respiratory cycle of a human being. Using a system of partial differential equations (PDEs) that models linear elasticity we compute displacements and stresses in a two-dimensional cross section of the diaphragm in its contracted state. The boundary data consists of a mix of displacement and traction conditions. If these are imposed as they are,

The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper, we systematically compute the solution landscapes of nonlinear constant/variable-order space-fractional problems on one- and two-dimensional rectangular domains. A fast approximation algorithm is developed to deal with the

This paper proposes an edge-detection-based method for discontinuous functions in multi-dimensional uncertainty propagation problems. We develop the Gegenbauer reconstruction method for multivariate functions to resolve the Gibbs phenomenon. To this end, we extend the concentration edge detector to approximate discontinuity hypersurfaces and use the Rosenblatt transformation to treat irregular space

We develop fifth-order A-WENO finite-difference schemes based on the path-conservative central-upwind method for nonconservative one- and two-dimensional hyperbolic systems of nonlinear PDEs. The main challenges in development of accurate and robust numerical methods for the studied systems come from the presence of nonconservative products. Semi-discrete second-order finite-volume path-conservative

Recent research efforts aimed at iteratively solving time-harmonic waves have focused on a broad range of techniques to accelerate convergence. In particular, for the famous Helmholtz equation, deflation techniques have been studied to accelerate the convergence of Krylov subspace methods. In this work, we extend the two-level deflation method to a multilevel deflation method for (heterogeneous) Helmholtz

Generating quasirandom points with high uniformity is a fundamental task in many fields. Existing number-theoretic approaches produce evenly distributed points in [0,1]d in asymptotic sense but may not yield a good distribution for a given set size. It is also difficult to extend those techniques to other geometries like a disk or a manifold. In this paper, we present a novel physics-informed framework

In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on curvilinear meshes using a generalization of flux differencing for numerical fluxes in fluctuation form. The method uses the skew-hybridized formulation of the element

We derive the Eulerian formulation for a peridynamic (PD) model of Newtonian viscous flow starting from fundamental principles: conservation of mass and momentum. This formulation is nonlocal, different from viscous flow models that utilize numerical methods like, e.g., the so-called “peridynamic differential operator” to approximate solutions of the classical Navier-Stokes equations. We show that

A simple Chimera grid method is developed for complex flows with moving boundaries. Based on the interpolation condition, a coupling strategy is proposed where algebraic equations are reconstructed to couple different domains. With respect to other methods, the coupling of different domains can be accomplished with the employment of any discretization scheme and the iterative process or the iterative

While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity

In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum entropy principle, the resulting approach can robustly resolve strong discontinuities with sub-element resolution, does not require problem-dependent parameter tuning

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture geometric features of computational domains, and using the mean squared residuals of the governing partial differential equations, boundary conditions, and sparse observations

Solving high-dimensional partial differential equations (PDEs) is a long-standing challenge, for which classical numerical methods suffer from the well-known curse of dimensionality. In this paper, we propose deep neural networks (NN) based temporal-difference (TD) learning methods for numerically solving high-dimensional parabolic PDEs. To this end, we approximate the solution of the original PDE

In this paper, an adaptive error-controlled hybrid fast solver that combines both O(N) and O(Nlog⁡N)schemes is proposed. For a given accuracy, the adaptive solver is used in the context of regularized vortex methods to optimize the speed of the velocity and vortex stretching calculation. This is accomplished by introducing criteria for cell division in building of the tree, conversion of multipole

In this study, we propose a sampling-type algorithm for a real-time identification of a set of short, linear perfectly conducting cracks in a two-dimensional bistatic measurement configuration. The indicator function is defined based on the asymptotic formula of the far-field pattern of the scattered field due to cracks. To clarify the applicability of the proposed algorithm, we investigate the mathematical

Divergence-free vector fields play an important role in many types of problems, including the incompressible Navier-Stokes equations and the equations for magnetohydrodynamics. In the discrete setting, these fields are often obtained by projection, resulting in a discrete approximation of the continuous field that is discretely divergence-free. For many applications, such as tracing particles, this

This work proposes an accurate hyper-singular boundary integral equation method for dynamic poroelastic problems with Neumann boundary condition in three dimensions and both the direct and indirect methods are adopted to construct combined boundary integral equations. The strongly-singular and hyper-singular integral operators are reformulated into compositions of weakly-singular integral operators

This paper describes a novel subface flux-based Finite Volume (FV) method for discretizing multi-dimensional hyperbolic systems of conservation laws of general unstructured grids. The subface flux numerical approximation relies on the notion of simple Eulerian Riemann solver introduced in the seminal work [G. Gallice; Positive and entropy stable Godunov-type schemes for gas dynamics and MHD equations

A novel approach to global gyrokinetic simulation is implemented in the flux-tube code stella. This is done by using a subsidiary expansion of the gyrokinetic equation in the perpendicular scale length of the turbulence, originally derived by Parra and Barnes [Plasma Phys. Controlled Fusion, 57 054003, 2015], which allows the use of Fourier basis functions while enabling the effect of radial profile

A novel Dynamic Mode Decomposition (DMD) technique capable of handling non–uniformly sampled data is proposed. As it is usual in DMD analysis, a linear relationship between consecutive snapshots is made. The performance of the new method, which we term θ-DMD, is assessed on three different, increasingly complex datasets: a synthetic flow field, a ReD=60 flow around a cylinder cross section, and a Reτ=200

A theoretical analysis of the entropy conservation properties is conducted to explain the different behaviors of the non-dissipative finite-difference spatial discretization schemes, such as the kinetic-energy and entropy preserving (KEEP) schemes. The analysis is conducted based on the spatially-discretized entropy-evolution equation derived from the Euler equations with retaining the discrete-level

The past two decades have borne remarkable progress in the application of the molecular dynamics method in a number of engineering problems. However, the computational efficiency is limited by the massive-atoms system, and the study of rare dynamically-relevant events is challenging at the timescale of molecular dynamics. In this work, a multi-scale molecular simulation algorithm is proposed with a

In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are used, for example, in the modelling of carbon market [1] and are linked to scalar conservation law perturbed by a diffusion. Classical FBSDEs methods fail to capture

For capillary driven flow the interface curvature is essential in the modelling of surface tension via the imposition of the Young–Laplace jump condition. We show that traditional geometric volume of fluid (VOF) methods, that are based on a piecewise linear approximation of the interface, do not lead to an interface curvature which is convergent under mesh refinement in time-dependent problems. Instead

The highly nonlinear nature of the system governing equations makes it difficult to simulate viscoelastic flows efficiently. In this paper, an implicit decoupling approach is proposed for the viscoelastic flow simulation with a monolithic projection method. The decoupling approach can be derived from the approximate block factorization at the matrix level, which has been successfully applied into the

Projection-based reduced order models (ROM) based on the weak form and the strong form of the discontinuous Galerkin (DG) method are proposed and compared for shock-dominated problems. The incorporation of dissipation components of DG in a consistent manner, including the upwinding flux and the localized artificial viscosity model, is employed to enhance stability of the ROM. To ensure efficiency,

Multi-objective Bayesian optimization (MOBO) is an efficient and robust optimization framework for expensive functions. In this work, we use MOBO to optimize the free parameters of a high-order nonlinear weighted essentially non-oscillatory (WENO) reconstruction scheme to devise a model for implicit large eddy simulations. We concurrently optimize for a low dispersion error and sufficient shock-capturing

A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of memory hierarchies, and solves it using parallel cyclic reduction on both distributed and shared memory. This method has a lower communication footprint across distributed memory partitions compared to conventional algorithms

Abstract not available

A high-order implicit radial basis function-based differential quadrature-finite volume (IRBFDQ-FV) method is presented in this work to efficiently simulate incompressible flows with heat transfer on unstructured mesh. The velocity and temperature fields are solved by locally using the lattice Boltzmann flux solver and the high-order finite volume method. Specifically, the proposed highly accurate

Large-scale simulations of time-dependent problems generate a massive amount of data and with the explosive increase in computational resources the size of the data generated by these simulations has increased significantly. This has imposed severe limitations on the amount of data that can be stored and has elevated the issue of input/output (I/O) into one of the major bottlenecks of high-performance

In this paper, we propose a flux correction technique generally applicable to practical finite-volume discretizations of a single flux evaluation per face for achieving second-order accuracy on arbitrary polyhedral grids involving non-planar faces. The proposed technique is derived from the k-exact finite-volume discretization approach originally introduced by Brenner. We take it as a general methodology

The ability to advance locally-stiff systems of equations in time depends on accurate and efficient temporal schemes. Recently, a new family of Paired Explicit Runge-Kutta (P-ERK) methods has been proposed. This approach allows different Runge-Kutta schemes with different numbers of active stages to be assigned based on local stiffness criteria. Whereas the original P-ERK formulation was only second-order

We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation

We study the time-dependent Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion, and we use the stochastic Galerkin method to extend the methodology from Kay et al. (2010) [21] into this framework. For the resulting stochastic problem, we explore

In this paper, Particle-in-Cell algorithms for the Vlasov–Poisson system are presented based on its Poisson bracket structure. The Poisson equation is solved by finite element methods, in which the appropriate finite element spaces are taken to guarantee that the semi-discretized system possesses a well defined discrete Poisson bracket structure. Then, splitting methods are applied to the semi-discretized

This paper presents a Bézier extraction based isogeometric topology optimization framework, in which the pseudo-densities and the weights at control points (CPs) are simultaneously treated as the design variables. A locally-adaptive smoothed density field, that is dynamically updated at each design iteration, is first proposed by utilizing the values of the non-uniform rational B-splines (NURBS) basis

In this work, we present a novel Lagrange–Galerkin method for the resolution of compressible and inviscid flows. The scheme considers: (i) high-order continuous space discretizations on unstructured triangular meshes, (ii) high-order implicit–explicit Runge-Kutta schemes for the time discretization, (iii) conservation of mass, momentum and total energy, as long as some integrals in the formulation

A well-known drawback of the Volume-Of-Fluid (VOF) method is that the breakup of thin liquid films or filaments is mainly caused by numerical aspects rather than by physical ones. The rupture of thin films occurs when their thickness reaches the order of the grid size and by refining the grid the breakup events are delayed. When thin filaments rupture, many droplets are generated due to the mass conserving

Interpolating unstructured data using barycentric coordinates becomes infeasible at high dimensions due to the prohibitive memory requirements of building a Delaunay triangulation. We present a new algorithm to construct ad-hoc simplices that are empirically guaranteed to contain the target coordinates, based on a nearest neighbor heuristic and an iterative dimensionality reduction through projection

A new Direct Numerical Simulation (DNS) code HAMISH with Adaptive Mesh Refinement (AMR) has been developed to simulate compressible reacting flow in a computationally economical manner. The focus is on problems where high gradients of temperature, density and species mass fraction remain localised, for example within the interior structure of flames. The resolution requirements of such local high-gradient

This paper presents a cell-centered Lagrangian method for the ideal magnetohydrodynamics (MHD) equations in two dimension. In order to compute the nodal velocity and the numerical fluxes through the cell interface, a 2D nodal approximate Riemann solver of HLLD-type is designed. The main new feature of the Riemann solver is two fast waves, two Alfvén waves and one entropy wave are considered for each

In this paper, high-order compact finite volume schemes on the unstructured grids based on the variational reconstruction are developed to solve the Reynolds averaged Navier-Stokes equations closed by the Spalart-Allmaras one-equation turbulence model. Encouraging progress is made in addressing the following two challenging problems: reducing the numerical errors on the large aspect ratio grids and

The Lax-Wendroff method is a single step method for evolving time dependent solutions governed by partial differential equations, in contrast to Runge-Kutta methods that need multiple stages per time step. We develop a flux reconstruction version of the method in combination with a Jacobian-free Lax-Wendroff procedure that is applicable to general hyperbolic conservation laws. The method is of collocation

In this study, we propose a new method that uses the recursive fitting method and wall function for the three-dimensional turbulent flow simulation. The recursive fitting method based on the Cartesian grid method is employed for the automatic generation around two- and three-dimensional geometries. The grid approximately represents the concave and convex features, i.e., a wing–fuselage juncture and

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A five-field mixed-primal finite element scheme is proposed solving for Stokes velocity-pressure and Biot displacement-total pressure-fluid pressure. Adequate inf-sup conditions

In this article, we first establish a new flow-coupled binary phase-field crystal model and prove its energy law. Then by using some newly introduced variables, we reformulate this three-phase model into an equivalent form, which makes it possible to construct a fully discrete linearized decoupling scheme with unconditional energy stability and second-order time accuracy to solve this model for the

Multiscale elliptic equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). The traditional homogenization techniques typically rely on the periodicity of the multiscale coefficients, thus finding the G-limits often requires sophisticated techniques in more general settings even when multiscale coefficient