A cubic B-spline quasi-interpolation method for solving two-dimensional unsteady advection diffusion equations

Abstract

Purpose

The purpose of this study is to extend the cubic B-spline quasi-interpolation (CBSQI) method via Kronecker product for solving 2D unsteady advection-diffusion equation. The CBSQI method has been used for solving 1D problems in literature so far. This study seeks to use the idea of a Kronecker product to extend the method for 2D problems.

Design/methodology/approach

In this work, a CBSQI is used to approximate the spatial partial derivatives of the dependent variable. The idea of the Kronecker product is used to extend the method for 2D problems. This produces the system of ordinary differential equations (ODE) with initial conditions. The obtained system of ODE is solved by strong stability preserving the Runge–Kutta method (SSP-RK-43).

Findings

It is found that solutions obtained by the proposed method are in good agreement with the analytical solution. Further, the results are also compared with available numerical results in the literature, and a reasonable degree of compliance is observed.

Originality/value

To the best of the authors’ knowledge, the CBSQI method is used for the first time for solving 2D problems and can be extended for higher-dimensional problems.

Citation

Mittal, R.C., Kumar, S. and Jiwari, R. (2020), "A cubic B-spline quasi-interpolation method for solving two-dimensional unsteady advection diffusion equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 9, pp. 4281-4306. https://doi.org/10.1108/HFF-07-2019-0597