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In the previous researches about the benchmark solutions in the irregular regions, there are some obvious shortcomings, such as small number of computational grids, simple computational domain, small characteristic number, and lack of mixed convection benchmark solution. In order to improve this situation, this article deeply studied the benchmark solutions for two-dimensional fluid flow and heat transfer problems in the irregular regions under the body-fitted coordinate system. Taking the lid-driven flow, natural convection, and mixed convection problems as the research objects and considering the influence of boundary configurations of the computational domains, Reynolds number, Prandtl number, and Grashof number, this article designed three groups of test cases. The program code is first verified through employing the nonlinear multigrid method based on the collocated finite volume method and then the numerical solutions of three test cases with 1024 × 1024 grids and convergence criterion of 10−14 are obtained to get the benchmark solutions estimated by the Richardson extrapolation method

Benchmark solutions for two-dimensional fluid flow and heat transfer problems in irregular regions using multigrid method