Parallel computation of the compressible Navier-Stokes equations

Computation and communication are the two main modules in parallel computing. Reducing communication beyond that required by the stability limit at the interfaces introduces errors into the solution, and a time-filtering technique is developed to damp these oscillations and yield an accurate solution. Computation on each processor can also be non-optimal depending upon the type of solution desired, transient or steady state. When a transient solution is desired, variable time-stepping techniques are introduced to reduce both computation and communication and yet satisfy accuracy requirements. For explicit, schemes, the CFL stability condition imposes a restriction on the time-step for the integration of the fluid flow equations inside a domain. For larger time-steps, the integration process turns unstable. By identifying the cause of the instability by means of a spectral decomposition, a filtering technique can be used leading to the suppression of these unstable spatial frequencies, while the other frequencies are integrated in a stable manner maintaining accuracy. To achieve stable and convergent parallel computations it is found that filtering the interface information between the blocks is also necessary. With a combination of block and interface filtering, high speedup and efficiency can be achieved. The NPARC code, which uses an explicit Runge-Kutta finite volume integration scheme, is parallelized by means of domain decomposition techniques and is used to demonstrate the developed parallel algorithms