A bounded scheme based on Bézier curves for convection-dominated transport problems

Abstract

This work presents a family of bounded schemes constructed based on the concept of Bézier curves that satisfies the TVD, CBC, and BAIR stability criteria for the numerical solution of convection-dominated transport problems in computational fluid dynamics problems. The convergence of the schemes to solve a series of 1D and 2D problems is analyzed. The numerical results of the proposed scheme are compared to other established methods from the literature. The numerical results show good agreement with exact solutions and numerical data from benchmarks. The findings of this work suggest the proposed family of methods as a promising alternative for solving convection-dominated problems.