THE TOTAL PRESSURE BOUNDARY-ELEMENT METHOD (TPBEM) FOR STEADY VISCOUS-FLOW PROBLEMS

The application of the boundary element method to viscous flow problem s is becoming increasingly important since it has offered great advant ages in the solid mechanics field. In the present research work, the t otal pressure boundary element method (TPBEM) is presented. The method offers favorable features for convective diffusion steady flow proble ms. The flow kinematics is described by a standard velocity-vorticity boundary domain integral representation while the integral equation fo r the kinetics is expressed in terms of velocity, vorticity and the to tal pressure at the boundary. The present scheme allows the BEM to be used in an optimal manner. This is achieved by applying an implicit-ex plicit numerical procedure. The implicit system of equations is writte n only for the boundary unknowns, vorticity and total pressure, while the other interior unknowns are computed explicitly by a standard unde r-relaxation procedure. This indeed greatly reduces the CPU time neede d to solve such a nonlinear viscous flow problem. Moreover, the comput ation of the total pressure at the boundary allows a direct determinat ion of the aerodynamic coefficients for solid boundaries. Effectivenes s and validity of the present TPBEM is illustrated by solving a standa rd benchmark driven cavity problem. Numerical results for Reynolds num bers 100 and 1000 show good agreement with other numerical solution an d experimental data. The present method consumes almost half of the CP U time needed for a standard finite difference solution.