| Summary: | A new, well posed, two-dimensional two-mode incompressible Kelvin{Helmholtz instability test
case has been chosen to explore the ability of a compressible algorithm, Godunov-type scheme
with the low Mach number correction, which can be used for simulations involving low Mach
numbers, to capture the observed vortex pairing process due to the initial Kelvin{Helmholtz
instability growth on low resolution grid. The order of accuracy, 2nd and 5th , of the compressible
algorithm is also highlighted.
The observed vortex pairing results and the corresponding momentum thickness of the mixing
layer against time are compared with results obtained using the same compressible algorithm but
without the low Mach number correction and three other methods, a Lagrange remap method
where the Lagrange phase is 2nd order accurate in space and time while the remap phase is 3rd
order accurate in space and 2nd order accurate in time, a 5th order accurate in space and time
nite di erence type method based on the wave propagation algorithm and a 5th order spatial
and 3rd order temporal accurate Godunov method utilising the SLAU numerical ux with low
Mach capture property.
The ability of the compressible ow solver of the commercial software, ANSYS Fluent, in solving
low Mach ows is also examined for both implicit and explicit methods provided in the compressible
ow 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 an
experiment conducted on the observation of vortex pairing process. Three di erent values of low
Mach numbers, 0:2, 0:02 and 0:002 have been tested on grid resolutions of 24 24, 32 32, 48 48
and 64 64 on all the di erent numerical approaches.
The results obtained show the vortex pairing process can be captured on a low grid resolution
with the low Mach number correction applied down to 0:002 with 2nd and 5th order Godunovtype
methods. Results also demonstrate clearly that a speci cally designed low Mach correction
or ux is required for all algorithms except the Lagrange-remap approach, where dissipation is
independent of Mach number. ANSYS Fluent's compressible ow solver with the implicit time
stepping method also captures the vortex pairing on low resolutions but excessive dissipation
prevents the instability growth when explicit time stepping method is applied.
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