Stable and Accurate Interpolation Operators for High-Order Multi-Block Finite-Difference Methods

TL;DR

This paper introduces new high-order interpolation operators for multi-block finite difference methods that ensure stability, accuracy, and conservation even with nonconforming grids, verified through eigenvalue analysis and simulations.

Contribution

The paper develops novel interpolation operators that preserve stability and accuracy across block interfaces in high-order finite difference schemes, addressing a key challenge in multi-block discretizations.

Findings

Operators maintain stability with eigenvalue analysis.

Operators preserve accuracy in Euler equation simulations.

Numerical results confirm conservation and stability.

Abstract

Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict stability, accuracy and conservation of the base scheme even when nonconforming grids or dissimilar operators are used in adjoining blocks. The stability properties of the new operators are verified using eigenvalue analysis, and the accuracy properties are verified using numerical simulations of the Euler equations in two spatial dimensions.