Application of Fourth-Order Explicit Schemes to the Computation of Axisymmetric Swirling Flows of Boussinesq Fluid in Containers with Arbitrary Cross Sections

Abstract

A higher-order numerical method is presented for the axisymmetric swirling flows of Boussinesq fluid in arbitrary-shaped containers with rotational symmetry. Explicit fourth-order finite-difference schemes on general curvilinear coordinates, a multigrid V-cycle method, and an optimized low-storage, fourth-order Runge-Kutta method are employed. The method is first tested by computing the vortex breakdown of uniform fluid in a cylindrical container. Numerical solutions are then presented for swirling flows in various shapes of container with temperature difference and buoyancy force. Good agreement with previous studies is demonstrated in these example problems, and higher-order accuracy is confirmed.