Related papers: Moment-based multi-resolution HWENO scheme for hyp…
We consider implementations of high-order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for the Euler equations in cylindrical and spherical coordinate systems with radial dependence only. The main concern of this…
A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions and in the meantime prevent spurious oscillations on solving hyperbolic conservation laws with long output times. Our…
In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order…
In this work, a framework to construct arbitrarily high-order low-dissipation shock-capturing schemes with flexible and controllable nonlinear dissipation for convection-dominated problems is proposed. While a set of candidate stencils of…
Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the…
A third-order weighted essentially non-oscillatory compact least-squares scheme is developed for the finite volume method on structured curvilinear non-uniform grids. The proposed scheme features compact least-squares reconstruction with…
In this study, a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called $\mathrm{P}_{n}\mathrm{T}_{m}-\mathrm{BVD}$ (polynomial of $n$-degree and THINC…
We propose a high order numerical scheme for time-dependent first order Hamilton--Jacobi--Bellman equations. In particular we propose to combine a semi-Lagrangian scheme with a Central Weighted Non-Oscillatory reconstruction. We prove a…
In this paper, a high-order multi-dimensional gas-kinetic scheme is presented for both inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation. Compared with the traditional ALE method, the flow variables are updated…
This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
In this work, a simple fourth-order accurate finite volume semi-discrete scheme is introduced to solve astrophysical magnetohydrodynamics (MHD) problems on Cartesian meshes. Hydrodynamic quantities like density, momentum and energy are…
In our previous work [29], we proposed a class of high-order asymptotic preserving (AP) finite difference weighted essentially non-oscillatory (WENO) schemes for solving the shallow water equations (SWEs) with bottom topography and Manning…
We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-discrete version of the proposed method is based on a technique…
In this paper, we develop bound-preserving (BP) finite-volume schemes for hyperbolic conservation laws on adaptive moving meshes. For scalar conservative laws, we rewrite the conventional high-order discretization as a convex combination of…
In this paper, we develop parametrized positivity satisfying flux limiters for the high order finite difference Runge-Kutta weighted essentially non-oscillatory (WENO) scheme solving compressible Euler equations to maintain positive density…
A novel approach for selecting appropriate reconstructions is implemented to the hyperbolic conservation laws in the high-order local polynomial-based framework, e.g., the discontinuous Galerkin (DG) and flux reconstruction (FR) schemes.…
In this paper, a class of high order numerical schemes is proposed for solving Hamilton-Jacobi (H-J) equations. This work is regarded as an extension of our previous work for nonlinear degenerate parabolic equations, see Christlieb et al.…
We propose an adaptive stencil construction for high order accurate finite volume schemes aposteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations. High-accuracy (up to the sixth-order presently) is achieved…
Entropy conditions play a crucial role in the extraction of a physically relevant solution for systems of conservation laws, thus motivating the construction of entropy stable schemes that satisfy a discrete analogue of such conditions.…