High Order Residual Distribution Conservative Finite Difference HWENO Scheme for Steady State Problems

04/14/2021
by   Jianfang Lin, et al.
0

In this paper, we develop a high order residual distribution (RD) method for solving steady state conservation laws in a novel Hermite weighted essentially non-oscillatory (HWENO) framework recently developed in [23]. In particular, we design a high order HWENO reconstructions for the integrals of source term and fluxes based on the point values of the solution and its spatial derivatives, and the principles of residual distribution schemes are adapted to obtain steady state solutions. The proposed novel HWENO framework enjoys two advantages. First, compared with the traditional HWENO framework, the proposed methods do not need to introduce additional auxiliary equations to update the derivatives of the unknown function, and compute them from the current value and the old spatial derivatives. This approach saves the computational storage and CPU time, which greatly improves the computational efficiency of the traditional HWENO framework. Second, compared with the traditional WENO method, reconstruction stencil of the HWENO methods becomes more compact, their boundary treatment is simpler, and the numerical errors are smaller at the same grid. Thus, it is also a compact scheme when we design the higher order accuracy, compared with that in [11] Chou and Shu proposed. Extensive numerical experiments for one and two-dimensional scalar and systems problems confirm the high order accuracy and good quality of our scheme.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/18/2021

High order finite difference Hermite WENO fixed-point fast sweeping method for static Hamilton-Jacobi equations

In this paper, we combine the nonlinear HWENO reconstruction in <cit.> a...
research
09/08/2020

High order finite difference Hermite WENO fast sweeping methods for static Hamilton-Jacobi equations

In this paper, we propose a novel Hermite weighted essentially non-oscil...
research
04/19/2023

A compact simple HWENO scheme with ADER time discretization for hyperbolic conservation laws I: structured meshes

In this paper, a compact and high order ADER (Arbitrary high order using...
research
05/30/2023

An absolutely convergent fixed-point fast sweeping WENO method on triangular meshes for steady state of hyperbolic conservation laws

High order fast sweeping methods for efficiently solving steady state so...
research
04/19/2023

Implicit high-order gas-kinetic schemes for compressible flows on three-dimensional unstructured meshes

In the previous studies, the high-order gas-kinetic schemes (HGKS) have ...
research
02/11/2019

Efficient Computation of High-Order Electromagnetic Field Derivatives for Multiple Design Parameters in FDTD

This paper introduces a new computational framework to derive electromag...
research
10/28/2016

Performance evaluation of explicit finite difference algorithms with varying amounts of computational and memory intensity

Future architectures designed to deliver exascale performance motivate t...

Please sign up or login with your details

Forgot password? Click here to reset