A div-curl-grad formulation for compressible buoyant flows solved by the least-squares finite element method
The paper reports the development of the least-squares finite element method for simulating compressible buoyant flows at low Mach numbers. We propose a div-curl-grad formulation with unknowns including vorticity, velocity, heat fluxes, temperature and pressure variation. The formulation is proved to be elliptic such that permissible boundary conditions become self-evident for a well posed flow problem. In contrast to conventional approaches, the present method evades the predicament of the `singularity' problem of low-speed flows, and no special treatment or artificial boundary condition is needed. Moreover, the assembled coefficient matrix is symmetric and positive-definite; its inversion is implemented by an element-by-element Jacobi conjugate gradient method. As a numerical example, we calculate two-dimensional compressible buoyant flows inside a square enclosure at various Rayleigh numbers.
element-by-element Jacobi conjugate gradient method
scientific article; zbMATH DE number 1057511
scientific article