Numerical Analysis of Compressible and Incompressible Turbulence Using High Order Finite Difference Method

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In this project, the direct numerical simulation codes based on the higher order method of lines are developed and the validations are carried out, in order to analyze the compressible and incompressible turbulences. To analyze the incompressible turbulence, the Navier-Stokes equations expressed by the primitive variables are solved by the variable order MAC method. The energy conservation is safisfied more exactly by using the interpolation method in the convective terms. Next, the new non-staggered finite difference method which satisfies the continuity equation at each time step and obtains the smooth pressure field, is proposed for solving the incompressible Navier-Stokes equations. This non-staggered finite difference method is extended to the body fitted coordinate system. Finaly, the 2-D homogeneous isotropic compressible turbulences are simulated by the higher order method of lines. In the weak shock turbulence, the compressible kinetic energy supplied by the internal energy is dominant and the shock waves are generated. On the other hand, the fluid is accelerated by the vortex motion and the shock waves are generated in the strong shock turbulence.