A mass-conservative higher-order ADI method for solving unsteady convection–diffusion equations

Advances in Difference Equations

Kanyuta Poochinapan¹  Nattakorn Sukantamala¹  Ben Wongsaijai¹ 

[1] Advanced Research Center for Computational Simulation, Chiang Mai University, 50200, Chiang Mai, Thailand;Department of Mathematics, Faculty of Science, Chiang Mai University, 50200, Chiang Mai, Thailand;Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., 10400, Bangkok, Thailand;

关键词: Mass-conservative;    High-order compact scheme;    Unsteady convection–diffusion equation;    Alternating direction implicit (ADI) method;   

DOI  :  10.1186/s13662-020-02885-6

来源: Springer

【 摘 要 】

In the paper, a high-order alternating direction implicit (ADI) algorithm is presented to solve problems of unsteady convection and diffusion. The method is fourth- and second-order accurate in space and time, respectively. The resulting matrix at each ADI computation can be obtained by repeatedly solving a penta-diagonal system which produces a computationally cost-effective solver. We prove that the proposed scheme is mass-conserved and unconditionally stable by means of discrete Fourier analysis. Numerical experiments are performed to validate the mass conservation and illustrate that the proposed scheme is accurate and reliable for convection-dominated problems.

【 授权许可】

CC BY