Numerical solution of two-dimensional problems of incompressible fluid convection in irregular domains

A finite-difference computational algorithm for solving the equations of convective flows of incompressible fluid in two-dimensional irregular domains using generalized curvilinear coordinates is constructed. The physical domain is mapped into a computational domain (unit square) in the space of generalized coordinates. The equations of mixed convection in primitive variables are written in generalized curvilinear coordinates and approximated in the computational domain on uniform non-staggered grids. The constructed computational algorithm is based on splitting difference schemes. The obtained results are mapped onto a nonuniform difference grid in the physical domain. The results of solving boundary value problems of heat and mass transfer of incompressible fluid in domains of complex shape are presented.