Related papers: New More Efficient A-WENO Schemes
In this paper, we propose a well-balanced fifth-order finite difference Hermite WENO (HWENO) scheme for the shallow water equations with non-flat bottom topography in pre-balanced form. For achieving the well-balance property, we adopt the…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
The essentially non-oscillatory (ENO) method is an efficient high order numerical method for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations, if existent, by adaptively choosing the local stencil for 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 note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. Under the assumption that the rarefaction curve of…
This paper deals with some qualitative properties of entropy solutions to hyperbolic conservation laws. In [11] the jump set of entropy solution to conservation laws has been introduced. We find an entropy solution to scalar conservation…
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…
This paper presents an extension of the hybrid scheme proposed by Wang et al. (J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible isotropic turbulence to flows with higher turbulent Mach numbers. The scheme still…
The blood flow model maintains the steady state solutions, in which the flux gradients are non-zero but exactly balanced by the source term. In this paper, we design high order finite difference weighted non-oscillatory (WENO) schemes to…
We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous…
In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes…
Embedded WENO methods utilize all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for…
We present THC: a new high-order flux-vector-splitting code for Newtonian and special-relativistic hydrodynamics designed for direct numerical simulations of turbulent flows. Our code implements a variety of different reconstruction…
In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…
The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled…
In this paper, we consider a nonlinear and nonlocal parabolic model for multi-species ionic fluids and introduce a semi-implicit finite volume scheme, which is second order accurate in space, first order in time and satisfies the following…
We are interested in the approximation of a steady hyperbolic problem. In some cases, the solution can satisfy an additional conservation relation, at least when it is smooth. This is the case of an entropy. In this paper, we show, starting…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a "post-processing algorithm", checking that…
Due to its excellent shock-capturing capability and high resolution, the WENO scheme family has been widely used in varieties of compressive flow simulation. However, for problems containing strong shocks and contact discontinuities, such…