Three-dimensional Characteristic Based Scheme and Artificial Compressibility Factor on Its Accuracy and Convergence

In this paper, the characteristics of three-dimensional incompressible flows were obtained along with artificial compressibility of Chorin. At first, compatibility equations and pseudo characteristics for three-dimensional flows were derived. Results showed that pseudo sound speed in incompressible flow is a function of compressibility parameter and the direction. The speed of sound is constant in compressible flows. By numerical solution of characteristics, four-dimensional pseudo hyper Mach cone was obtained. A code in MATLAB has been written to obtain numerical solution. In two-dimensional flows, one has three-dimensional Mach cone, instead of four dimensional one. This cross section is circle for compressible flows. In this work, natural and forced convections, were simulated in different dimensionless numbers: Reynolds, Prandtl, and Nusselt numbers. For these simulations, a new code has been written in FORTRAN. In the last part of this research, the influence of compressible parameter on accuracy and convergence was surveyed.