High Order Boundary Extrapolation Technique for Finite Difference Methods on Complex Domains with Cartesian Meshes

Abstract

The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the numerical methods and mesh type. In this paper we present a technique for the extrapolation of information from the interior of the computational domain to ghost cells designed for structured Cartesian meshes (which, as opposed to non-structured meshes, cannot be adapted to the morphology of the domain boundary). This technique is based on the application of Lagrange interpolation with a filter for the detection of discontinuities that permits a data dependent extrapolation, with higher order at smooth regions and essentially non oscillatory properties near discontinuities.

Cited by in corpus (5)

• Very high-order Cartesian-grid finite difference method on arbitrary geometries
• High Order Weighted Extrapolation for Boundary Conditions for Finite Difference Methods on Complex Domains with Cartesian Meshes
• Towards pore-scale simulation of combustion in porous media using a low-Mach hybrid lattice Boltzmann/finite difference solver
• On the relation of powerflow and Telegrapher's equations: continuous and numerical Lyapunov stability
• High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles