High-order ADI schemes for convection-diffusion equations with mixed derivative terms

TL;DR

This paper introduces high-order ADI schemes for convection-diffusion equations with mixed derivatives, achieving fourth-order spatial accuracy and second-order temporal accuracy, based on a stable ADI framework.

Contribution

It develops new high-order ADI schemes that are unconditionally stable and more accurate for convection-diffusion equations with mixed derivatives.

Findings

Schemes are fourth-order accurate in space.

Schemes are second-order accurate in time.

Unconditionally stable ADI approach used.

Abstract

We present new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with mixed derivative terms. Our approach is based on the unconditionally stable ADI scheme proposed by Hundsdorfer. Different numerical discretizations which lead to schemes which are fourth-order accurate in space and second-order accurate in time are discussed.