A multi-GPU based accurate algorithm for simulations of gas-liquid flows

Numerical simulation of gas-liquid flows with large variations in density across the interfaces is of considerable importance to the study of multiphase flows. However, a common difficulty in such simulations is the accurate resolution of the interface and the imposition of the surface tension force across the interface. It is well known that if the interfacial forces are not represented accurately, large spurious velocities are generated which can completely degrade the fidelity of the calculations. We have recently developed a high-performance CFD code using a novel numerical method proposed by Wang and Tong [1] to implement the surface tension force. In this method the surface tension force is modeled as a gradient of a pressure field (p₁), which is computed by solving an additional pressure Poisson equation (PPE). This new PPE has the pressure jump condition across the interface as a local source term at the interface and is solved with Neumann boundary conditions. The traditional pressure field that ensures a divergence-free velocity field is determined in the regular way by solving another pressure Poisson equation. We have implemented this strategy in a multi-GPU based Navier-Stokes solver (CUFLOW [2-4]) developed in our laboratory. With our in-house 4-GPU workstation we are able to do calculations with up to 80 million control volumes. In this paper, we present the details of the numerical algorithm, multi GPU implementation, speed-up and computations of static bubble in liquid pool and a bubble rising in a square duct.