High-order ADI schemes for convection-diffusion equations with mixed derivative terms
This work provides more accurate numerical methods for solving convection-diffusion equations, which are important in various engineering and scientific applications.
The authors developed new high-order ADI schemes for convection-diffusion equations with mixed derivative terms, achieving fourth-order accuracy in space and second-order in time.
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.