Three-dimensional characteristic approach for incompressible thermo-flows and influence of artificial compressibility parameter

In this paper the characteristics of unsteady three-dimensional incompressible flows with heat transfer are obtained along with artificial compressibility of Chorin. At first, compatibility equations and pseudo characteristics for three-dimensional flows are derived from five governing equations (continuity equation, Momentum equations in three directions, and energy equation) and then results are simplified to two dimensional flows. Pseudo Mach hyper-cone (four dimensional cone) are found and its cross-section with physical axis is calculated numerically. Unlike compressible flow, this is not a sphere. It is found that the pseudo acoustic speed within the incompressible flow is function of artificial compressibility parameter and the directions. In two dimensional, Pseudo Mach cone is obtained by numerical solution of characteristic equations. Unlike compressible flow, the cross section of Mach cone with x-y plane is not circle. This shape is not oval, too. The influence of artificial compressibility parameter on convergence history and accuracy was surveyed by simulation of cavity flow as a benchmark