A new, well posed, two-dimensional two-mode incompressible Kelvin{Helmholtz instability testcase has been chosen to explore the ability of a compressible algorithm, Godunov-type schemewith the low Mach number correction, which can be used for simulations involving low Machnumbers, to capture the observed vortex pairing process due to the initial Kelvin{Helmholtzinstability growth on low resolution grid. The order of accuracy, 2nd and 5th , of the compressiblealgorithm is also highlighted.The observed vortex pairing results and the corresponding momentum thickness of the mixinglayer against time are compared with results obtained using the same compressible algorithm butwithout the low Mach number correction and three other methods, a Lagrange remap methodwhere the Lagrange phase is 2nd order accurate in space and time while the remap phase is 3rdorder accurate in space and 2nd order accurate in time, a 5th order accurate in space and timenite di erence type method based on the wave propagation algorithm and a 5th order spatialand 3rd order temporal accurate Godunov method utilising the SLAU numerical ux with lowMach capture property.The ability of the compressible ow solver of the commercial software, ANSYS Fluent, in solvinglow Mach ows is also examined for both implicit and explicit methods provided in the compressibleow solver.In the present two dimensional two mode incompressible Kelvin{Helmholtz instability test case,the ow conditions, stream velocities, length-scales and Reynolds numbers, are taken from anexperiment conducted on the observation of vortex pairing process. Three di erent values of lowMach numbers, 0:2, 0:02 and 0:002 have been tested on grid resolutions of 24 24, 32 32, 48 48and 64 64 on all the di erent numerical approaches.The results obtained show the vortex pairing process can be captured on a low grid resolutionwith the low Mach number correction applied down to 0:002 with 2nd and 5th order Godunovtypemethods. Results also demonstrate clearly that a speci cally designed low Mach correctionor ux is required for all algorithms except the Lagrange-remap approach, where dissipation isindependent of Mach number. ANSYS Fluent's compressible ow solver with the implicit timestepping method also captures the vortex pairing on low resolutions but excessive dissipationprevents the instability growth when explicit time stepping method is applied.
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