First order hyperbolic approach for Anisotropic Diffusion equation
arXiv:1907.11897 · doi:10.1016/j.jcp.2019.06.064
Abstract
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 scheme that is independent of the degree of anisotropy is made straightforward by the hyperbolic method with an optimal length scale. We demonstrate that the gradients are computed simultaneously to the same order of accuracy as that of the solution variable by using weight compact finite difference schemes. Furthermore, the approach is extended to improve further the simulation of the magnetized electrons test case previously discussed in Refs.[J. Comput. Phys., 284 (2015) 59-69 and 374 (2018) 1120-1151]. Numerical results indicate that these schemes are capable of delivering high accuracy and the proposed approach is expected to allow the hyperbolic method to be successfully applied to a wide variety of linear and nonlinear problems with anisotropic diffusion.
arXiv comment32 pages, 13 figures, 6 tables
References in corpus (7)
- Preserving Monotonicity in Anisotropic Diffusion
- High-Order Localized Dissipation Weighted Compact Nonlinear Scheme for Shock- and Interface-Capturing in Compressible Flows
- An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition
- An asymptotic preserving scheme for strongly anisotropic elliptic problems
- A hyperbolic-equation system approach for magnetized electron fluids in quasi-neutral plasmas
- A flux-splitting method for hyperbolic-equation system of magnetized electron fluids in quasi-neutral plasmas
- High-order upwind and non-oscillatory approach for steady state diffusion, advection-diffusion and application to magnetized electrons
Cited by in corpus (5)
- High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm
- Efficient high-order Gradient-based Reconstruction for compressible flows
- Wave or Physics-Appropriate Multidimensional Upwinding Approach for Compressible Multiphase Flows
- Consistent Interface Capturing Adaptive Reconstruction Approach for Viscous Compressible Multicomponent Flows
- High-order flux reconstruction method for the hyperbolic formulation of the incompressible Navier-Stokes equations on unstructured grids