相关论文: A high-order weighted finite difference scheme wit…
We propose a high resolution finite volume scheme for a (m+1)x(m+1) system of non strictly hyperbolic conservation laws which models multicomponent polymer flooding in enhanced oil-recovery process in two dimensions. In the presence of…
An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as…
In this paper, we develop a new free-stream preserving (FP) method for high-order upwind conservative finite-difference (FD) schemes on the curvilinear grids. This FP method is constrcuted by subtracting a reference cell-face flow state…
A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
In this paper, we introduce a high-order tensor-train (TT) finite volume method for the Shallow Water Equations (SWEs). We present the implementation of the $3^{rd}$ order Upwind and the $5^{th}$ order Upwind and WENO reconstruction schemes…
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two…
In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite…
In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…
In this paper we analyze a fully discrete scheme for a general Cahn-Hilliard equation coupled with a nonsteady Magneto-hydrodynamics flow, which describes two immiscible, incompressible and electrically conducting fluids with different…
In this paper, we propose a high order semi-implicit well-balanced finite difference scheme for all Mach Euler equations with a gravitational source term. To obtain the asymptotic preserving property, we start from the conservative form of…
We extend the recently introduced explicit divergence-free DG scheme for incompressible hydrodynamics [arXiv:1808.04669]. to the incompressible magnetohydrodynamics (MHD). A globally divergence-free finite element space is used for both the…
In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented. The scheme belongs to the family of ADER methods where the Generalized Riemann Problems (GRP) is a building block. The…
We study in this paper three variants of the high-order Discontinuous Galerkin (DG) method with Runge-Kutta (RK) time integration for the induction equation, analysing their ability to preserve the divergence free constraint of the magnetic…
In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity $\nu$ in an axis-aligned domain $\Omega$. We decouple the velocity $\bm u$ and pressure $p$ by deriving a novel biharmonic…
The collocation method uses the Rhie-Chow scheme to find the cell interface velocity by pressure-weighted interpolation. The accuracy of this interpolation method in unsteady flows has not been fully clarified. This study constructs a…
We introduce a Hybrid High-Order (HHO) method for the Schr\"odinger equation in the presence of a magnetic vector potential. In quantum mechanics, physical observables are invariant under continuous gauge transformations, which must be kept…
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one…
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…
We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new…