The total pressure boundary element method (TPBEM) for steady viscous flow problems

Abstract

The application of the boundary element method to viscous flow problems is becoming increasingly important since it has offered great advantages in the solid mechanics field. In the present research work, the total pressure boundary element method (TPBEM) is presented. The method offers favorable features for convective diffusion steady flow problems. The flow kinematics is described by a standard velocity-vorticity boundary domain integral representation while the integral equation for the kinetics is expressed in terms of velocity, vorticity and the total pressure at the boundary. The present scheme allows the BEM to be used in an optimal manner. This is achieved by applying an implicit-explicit numerical procedure. The implicit system of equations is written only for the boundar unknowns, vorticity and total pressure, while the other interior unknowns are computed explicitly by a standard under-relaxation procedure. This indeed greatly reduces the CPU time needed to solve such a nonlinear viscous flow problem. Moreover, the computation of the total pressure at the boundary allows a direct determination of the aerodynamic coefficients for solid boundaries. Effectiveness and validity of the present TPBEM is illustrated by solving a standard benchmark driven cavity problem. Numerical results for Reynolds numbers 100 and 1000 show good agreement with other numerical solution and experimental data. The present method consumes almost half of the CPU time needed for a standard finite difference solution.