Application of the Double Potential Method to Simulate Incompressible Viscous Flows

摘要

In this paper we discuss an application of the double potential method for modelling flow of incompressible fluid. This method allows us to avoid the known difficulties in calculating pressure and overcome the instability of numerical solution. Also, the double potential method enables us to simplify the problem of boundary conditions setting. It arises when computing the incompressible fluid flow by the Navier-Stokes equations in the vector potential - velocity rotor variables. In the approach given, the final system of equations is approximated through applying the finite volume method. In this case, an exponential transformation of the flow terms is applied. A parallel program was developed by means of using MPI and OpenMP technologies for the purpose of the numerical method computer implementation. We used two tasks to test. One of them deals with the classical calculation of the fluid flow establishment in a long round pipe. The other one is connected with the flow calculation in the pipe that in the output region contains a separation into two symmetrical parts. To perform numerical simulation, we take into consideration the steady flow with Reynolds numbers of 50 and 100. The numerical results obtained are consistent with computational results received through using the ANSYS CFD package.