Visualizing Non-Equilibrium Flow Simulations using 3-D Velocity Distribution Functions

Scientific visualization techniques have been used to probe and understand better the physics of non-equilibrium flows. A visualization methodology for non-equilibrium flow simulations using 3-D velocity distribution functions(VDFs) is illustrated in application to various non-equilibrium flow problems. A one-dimensional normal shock wave problem is considered for two different upstream Mach numbers corresponding to weak and strong non-equilibrium flow conditions. The iso-surfaces of 3-D VDFs inside the shock wave obtained using various solution techniques including the ES-BGK method, DSMC technique, Mott-Smith solution, and the Navier-Stokes(NS) distribution functions using Chapman-Enskog theory are compared and contrasted. The visualization technique is extended to two-dimensional hypersonic flow at M = 10 past a flat plate with sharp leading edge by comparing the isosurfaces of 3-D NS VDFs obtained at three different locations in the flowfield. The visualization of 3-D VDFs is shown to provide valuable information about the degree and direction of non-equilibrium for both 1-D and 2-D flows.