Multi-domain hybrid spectral-WENO methods for hyperbolic conservation laws

Authors:
Bruno Costa;Wai Sun Don
Affiliations:
Departamento de Matemática Aplicada, IM-UFRJ, Caixa Postal 68530, Rio de Janeiro, RJ, C.E.P. 21945-970, Brazil;Division of Applied Mathematics, Brown University, Providence, RI 02912, United States
Venue:
Journal of Computational Physics
Year:
2007

Citing 9
Cited 4

Convergence of spectral methods for nonlinear conservation laws

SIAM Journal on Numerical Analysis
Legendre pseudospectral viscosity method for nonlinear conservation laws

SIAM Journal on Numerical Analysis
Numerical study of pseudospectral methods in shock wave applications

Journal of Computational Physics
Adaptive multiresolution schemes for shock computations

Journal of Computational Physics
Accuracy and speed in computing the Chebyshev collocation derivative

SIAM Journal on Scientific Computing
Efficient implementation of weighted ENO schemes

Journal of Computational Physics
Multidomain WENO Finite Difference Method with Interpolation at Subdomain Interfaces

Journal of Scientific Computing
Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon

Journal of Computational and Applied Mathematics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points

Journal of Computational Physics

A massively parallel multi-block hybrid compact-WENO scheme for compressible flows

Journal of Computational Physics
High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws

Journal of Computational Physics
A class of finite difference schemes with low dispersion and controllable dissipation for DNS of compressible turbulence

Journal of Computational Physics
Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws

Journal of Computational Physics

Quantified Score

Hi-index	31.47

Visualization

Abstract

In this paper, we introduce the multi-domain hybrid Spectral-WENO method aimed at the discontinuous solutions of hyperbolic conservation laws. The main idea is to conjugate the non-oscillatory properties of the high order weighted essentially non-oscillatory (WENO) finite difference schemes with the high computational efficiency and accuracy of spectral methods. Built in a multi-domain framework, subdomain adaptivity in space and time is used in order to maintain the solutions parts exhibiting high gradients and discontinuities always inside WENO subdomains, while the smooth parts of the solution are kept in spectral ones. A high order multi-resolution algorithm by Ami Harten is used to determine the smoothness of the solution in each subdomain. Numerical experiments with the simulation of compressible flow in the presence of shock waves are performed.