Boundary condition is one of the major factors to influence the numerical stability and solution accuracy in numerical analysis. One of the most important physical boundary conditions in the flow field analysis is the wall boundary condition imposed on the body surfaces. To solve a three-dimensional compressible Euler equation (with five coupled PDE’s), totally five boundary conditions at the body surfaces should be prescribed. The momentum equation in the direction normal to the inviscid solid wall provides the pressure at the surface of the wall. For the cases with no-heat source or sink, the total temperature at the wall and the incoming flow should remain constant, when the steady condition is prevailed. The no-penetration condition through the solid wall and slip condition provides an equation relating the three velocity components. Assuming identical flow direction at the wall with the adjacent node, the last thing is the velocity magnitude that should be cast in such a way to give accurate, stable and robust solution. In this paper, four different methods for calculation of the wall velocity magnitude are proposed and applied to an identical test case of subsonic and supersonic flows such as: (1) Inviscid flow in a 3D converging-diverging nozzle, (2) Inviscid subsonic flow in a single 90° elbow, (3) Inviscid supersonic flow over a wedge, and (4) Inviscid flow through a compressor blade geometry of NACA 65410. A recently implemented 3D in-house CFD code (based on the flux difference splitting scheme of Roe (1981)) is used to compute compressible flows in generalized coordinates. It is found that the way to specify the additional numerical wall boundary condition strongly affects the overall stability and accuracy of the solution. It is concluded that there is no best boundary condition to cover all of the test cases, but the best wall boundary condition should be introduced very carefully for each type of flow.
Consistent Wall Boundary Condition for Lattice-Boltzmann Method.
