相关论文: Provably Stable Flux Reconstruction High-Order Met…

This paper proposes an Arbitrary Lagrangian-Eulerian incompressible finite volume scheme based on Consistent Flux Reconstruction method (ALE-CFR) on deforming two-dimensional unstructured triangular grids. The scheme is further applied to…

We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with…

This paper extends the gradient-based reconstruction approach of Chamarthi \cite{chamarthi2023gradient} to genuine high-order accuracy for inviscid test cases involving smooth flows. A seventh-order accurate scheme is derived using the same…

Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…

We present a systematical approach to developing arbitrarily high order, unconditionally energy stable numerical schemes for thermodynamically consistent gradient flow models that satisfy energy dissipation laws. Utilizing the energy…

This paper concerns preservation of velocity and pressure equilibria in smooth, compressible, multicomponent flows in the inviscid limit. First, we derive the velocity-equilibrium and pressure-equilibrium conditions of a standard…

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics)…

In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can…

A simple flux reconstruction for finite element solutions of reaction-diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction-diffusion problem. The…

This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an…

We propose a local discontinuous Galerkin (LDG) method for the fractional Korteweg-de Vries (KdV) equation, involving the fractional Laplacian with exponent $\alpha \in (1,2)$ in one and multiple space dimensions. By decomposing the…

This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…

The accurate numerical simulation of high Reynolds number incompressible flows is a challenging topic in computational fluid dynamics. Classical inf-sup stable methods like the Taylor-Hood element or only $L^2$-conforming discontinuous…

We consider the Dynamical Low Rank (DLR) approximation of random parabolic equations and propose a class of fully discrete numerical schemes. Similarly to the continuous DLR approximation, our schemes are shown to satisfy a discrete…

This article aims at presenting a new local subcell monolithic Discontinuous-Galerkin/Finite-Volume (DG/FV) convex property preserving scheme solving system of conservation laws on 2D unstructured grids. This is known that DG method needs…

The discontinuous Galerkin (DG) method is an established method for computing approximate solutions of partial differential equations in many applications. Unlike continuous finite elements, in DG methods, numerical fluxes are used to…

High-order numerical methods for unstructured grids combine the superior accuracy of high-order spectral or finite difference methods with the geometric flexibility of low-order finite volume or finite element schemes. The Flux…

In this paper, we first propose a filter-based continuous Ensemble Eddy Viscosity (EEV) model for stochastic turbulent flow problems. We then propose a generic algorithm for a family of fully discrete, grad-div regularized, efficient…

Compact Runge-Kutta (cRK) Discontinuous Galerkin (DG) methods, recently introduced in [Q. Chen, Z. Sun, and Y. Xing, SIAM J. Sci. Comput. SIAM J. Sci. Comput., 46: A1327-A1351, 2024], are a variant of RKDG methods for solving hyperbolic…

This paper develops the high-order entropy stable (ES) finite difference schemes for multi-dimensional compressible Euler equations with the van der Waals equation of state (EOS) on adaptive moving meshes. Semi-discrete schemes are first…