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

TL;DR

This paper introduces a high-order boundary extrapolation method for finite difference schemes on complex domains with Cartesian meshes, enabling accurate and non-oscillatory boundary conditions for hyperbolic conservation laws.

Contribution

It presents a novel Lagrange interpolation-based extrapolation technique with filtering for structured Cartesian meshes, improving boundary treatment on complex geometries.

Findings

Achieves higher order accuracy in smooth regions

Reduces oscillations near discontinuities

Effective for hyperbolic conservation laws on complex domains

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.