Related papers: Moment-based multi-resolution HWENO scheme for hyp…
We present a new multidimensional classical hydrodynamics code based on Semidiscrete Central Godunov-type schemes and high order Weighted Essentially Non-oscillatory (WENO) data reconstruction. This approach is a lot simpler and easier to…
We present a high-order conservative, positivity-preserving, and non-oscillatory scheme for solving the Vlasov equation. The scheme attains formal fifth-order accuracy through a convex combination of positive and non-oscillatory polynomials…
We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is…
In this paper, we introduce a superconvergent approximation method that employs radial basis functions (RBFs) in the numerical solution of conservation laws. The use of RBFs for interpolation and approximation is a well developed area of…
In the previous studies, the high-order gas-kinetic schemes (HGKS) have achieved successes for unsteady flows on three-dimensional unstructured meshes. In this paper, to accelerate the rate of convergence for steady flows, the implicit…
A high order finite difference method is proposed for unstructured meshes to simulate compressible inviscid/viscous flows with/without discontinuities. In this method, based on the strong form equation, the divergence of the flux on each…
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth…
When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For…
A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin…
We study experimental convergence rates of three shock-capturing schemes for hyperbolic systems of conservation laws: the second-order central-upwind (CU) scheme, the third-order Rusanov-Burstein-Mirin (RBM), and the fifth-order alternative…
In this work, we construct a fifth-order weighted essentially non-oscillatory (WENO) scheme with exponential approximation space for solving dispersive equations. A conservative third-order derivative formulation is developed directly using…
This paper introduces a memory-reduction third-order compact gas-kinetic scheme (CGKS) for solving compressible Euler and Navier-Stokes equations on 3D unstructured meshes. The scheme utilizes a time-evolution gas distribution function to…
In this work, high-order discrete well-balanced methods for one-dimensional hyperbolic systems of balance laws are proposed. We aim to construct a method whose discrete steady states correspond to solutions of arbitrary high-order ODE…
In this paper, we present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The method combines the efficiency of linear reconstruction with the robustness of high-order…
The weighted essentially non-oscillatory (WENO) schemes are widely used for hyperbolic conservation laws due to the ability to resolve discontinuities and maintain high-order accuracy in smooth regions at the same time. For hyperbolic…
In \cite{christlieb2019kernel}, the authors developed a class of high-order numerical schemes for the Hamilton-Jacobi (H-J) equations, which are unconditionally stable, yet take the form of an explicit scheme. This paper extends such…
Due to the prevalence of magnetic fields in astrophysical environments, magnetohydrodynamic (MHD) simulation has become a basic tool for studying astrophysical fluid dynamics. To further advance the precision of MHD simulations, we have…
In this paper we extensively study the stochastic Galerkin scheme for uncertain systems of conservation laws, which appears to produce oscillations already for a simple example of the linear advection equation with Riemann initial data.…
The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrich splitting, the WENO reconstruction, the…
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…