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

In this paper, obtaining the characteristics of unsteady three-dimensional incompressible flows with heat transfer along with artificial compressibility of chorin is investigated. 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) is 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 a function of the artificial compressibility parameter and the directions. in two-dimensional flow, pseudo mach cone is obtained by numerical solution of characteristic equations. unlike compressible flow, the cross-section of mach cone with the x-y plane is not a circle. this shape is not oval, too. the influence of artificial compressibility parameter on convergence history and accuracy is surveyed by simulation of cavity flow as a benchmark.