Nearly incompressible fluids with inhomogeneous background : simulation results

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7839 Nonlinear Phenomena (4400, 6944), 7863 Turbulence (4490)

Scientific paper

Previously, we generalized the nearly incompressible theory to flows which include the large-scale inhomogeneous background (e.g. the solar wind flow). This leads to the description which already at the lowest order contains non-solenoidal velocity fluctuations and where density fluctuations behave like a passive scalar. Locally (for small length scales) this system of equations converge to the usual incompressible equations and therefor we call them 'locally incompressible'. In this poster, we further investigate the obtained 'locally incompressible' system by direct numerical simulation. In present time our 2D code is based on the modified Marker and Cell (MAC) method developed on the staggered grid. Static large-scale background is assumed to have constant speed in horizontal direction, together with significant gradient in density. MAC method uses solution of the Poisson equation for pressure in each time step, but because of non-periodicity in horizontal direction, fast fourier transform (FFT) Poisson solvers can not be used. We instead incorporate successive over relaxation (SOR) or alternative direction implicit (ADI) techniques. For comparison we are examining two different sets of boundary conditions in horizontal direction, one as a inflow-outflow boundaries, the other as a 'periodic boundaries with compression'. Our preliminary low-resolution results indicates the formation of Kolmogorov spectra, together with dissipation of total energy contained in vortical modes, whereas the total energy contained in solenoidal modes after initial drop remains constant. For higher resolution results we are working on optimization and parallel version of the code.

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