Semi-conservative reduced speed of sound technique for low Mach number flows with large density variations. (arXiv:1812.04135v1 [physics.comp-ph])
<a href="http://arxiv.org/find/physics/1/au:+Iijima_H/0/1/0/all/0/1">H. Iijima</a>, <a href="http://arxiv.org/find/physics/1/au:+Hotta_H/0/1/0/all/0/1">H. Hotta</a>, <a href="http://arxiv.org/find/physics/1/au:+Imada_S/0/1/0/all/0/1">S. Imada</a>
The reduced speed of sound technique (RSST) has been used for efficient
simulation of low Mach number flows in solar and stellar convection zones. The
basic RSST equations are hyperbolic, and are suitable for parallel computation
by domain decomposition. The application of RSST is limited to cases where
density perturbations are much smaller than the background density. In
addition, non-conservative variables are required to be evolved using this
method, which is not suitable in cases where discontinuities like shock waves
co-exist in a single numerical domain. In this study, we suggest a new
semi-conservative formulation of the RSST that can be applied to low Mach
number flows with large density variations. We derive the wave speed of the
original and newly suggested methods to clarify that these methods can reduce
the speed of sound without affecting the entropy wave. The equations are
implemented using the finite volume method. Several numerical tests are carried
out to verify the suggested methods. The analysis and numerical results show
that the original RSST is not applicable when mass density variations are
large. In contrast, the newly suggested methods are found to be efficient in
such cases. We also suggest variants of the RSST that conserve momentum in the
machine precision. The newly suggested variants are formulated as
semi-conservative equations, which reduce to the conservative form of the Euler
equations when the speed of sound is not reduced. This property is advantageous
when both high and low Mach number regions are included in the numerical
domain. The newly suggested forms of RSST can be applied to a wider range of
low Mach number flows.
The reduced speed of sound technique (RSST) has been used for efficient
simulation of low Mach number flows in solar and stellar convection zones. The
basic RSST equations are hyperbolic, and are suitable for parallel computation
by domain decomposition. The application of RSST is limited to cases where
density perturbations are much smaller than the background density. In
addition, non-conservative variables are required to be evolved using this
method, which is not suitable in cases where discontinuities like shock waves
co-exist in a single numerical domain. In this study, we suggest a new
semi-conservative formulation of the RSST that can be applied to low Mach
number flows with large density variations. We derive the wave speed of the
original and newly suggested methods to clarify that these methods can reduce
the speed of sound without affecting the entropy wave. The equations are
implemented using the finite volume method. Several numerical tests are carried
out to verify the suggested methods. The analysis and numerical results show
that the original RSST is not applicable when mass density variations are
large. In contrast, the newly suggested methods are found to be efficient in
such cases. We also suggest variants of the RSST that conserve momentum in the
machine precision. The newly suggested variants are formulated as
semi-conservative equations, which reduce to the conservative form of the Euler
equations when the speed of sound is not reduced. This property is advantageous
when both high and low Mach number regions are included in the numerical
domain. The newly suggested forms of RSST can be applied to a wider range of
low Mach number flows.
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