227,709 research outputs found
Low Mach number effect in simulation of high Mach number flow
In this note, we relate the two well-known difficulties of Godunov schemes:
the carbuncle phenomena in simulating high Mach number flow, and the inaccurate
pressure profile in simulating low Mach number flow. We introduced two simple
low-Mach-number modifications for the classical Roe flux to decrease the
difference between the acoustic and advection contributions of the numerical
dissipation. While the first modification increases the local numerical
dissipation, the second decreases it. The numerical tests on the double-Mach
reflection problem show that both modifications eliminate the kinked Mach stem
suffered by the original flux. These results suggest that, other than
insufficient numerical dissipation near the shock front, the carbuncle
phenomena is strongly relevant to the non-comparable acoustic and advection
contributions of the numerical dissipation produced by Godunov schemes due to
the low Mach number effect.Comment: 9 pages, 1 figur
Low Mach number flows, and combustion
We prove uniform existence results for the full Navier-Stokes equations for
time intervals which are independent of the Mach number, the Reynolds number
and the P\'eclet number. We consider general equations of state and we give an
application for the low Mach number limit combustion problem introduced by
Majda
Low Mach Number Modeling of Type Ia Supernovae
We introduce a low Mach number equation set for the large-scale numerical
simulation of carbon-oxygen white dwarfs experiencing a thermonuclear
deflagration. Since most of the interesting physics in a Type Ia supernova
transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a
considerable increase in accuracy and savings in computer time compared with
frequently used compressible codes. Our equation set is derived from the fully
compressible equations using low Mach number asymptotics, but without any
restriction on the size of perturbations in density or temperature. Comparisons
with simulations that use the fully compressible equations validate the low
Mach number model in regimes where both are applicable. Comparisons to
simulations based on the more traditional anelastic approximation also
demonstrate the agreement of these models in the regime for which the anelastic
approximation is valid. For low Mach number flows with potentially finite
amplitude variations in density and temperature, the low Mach number model
overcomes the limitations of each of the more traditional models and can serve
as the basis for an accurate and efficient simulation tool.Comment: Accepted for publication in the Astrophysical Journal 31 pages, 5
figures (some figures degraded in quality to conserve space
A Low Mach Number Model for Moist Atmospheric Flows
We introduce a low Mach number model for moist atmospheric flows that
accurately incorporates reversible moist processes in flows whose features of
interest occur on advective rather than acoustic time scales. Total water is
used as a prognostic variable, so that water vapor and liquid water are
diagnostically recovered as needed from an exact Clausius--Clapeyron formula
for moist thermodynamics. Low Mach number models can be computationally more
efficient than a fully compressible model, but the low Mach number formulation
introduces additional mathematical and computational complexity because of the
divergence constraint imposed on the velocity field. Here, latent heat release
is accounted for in the source term of the constraint by estimating the rate of
phase change based on the time variation of saturated water vapor subject to
the thermodynamic equilibrium constraint. We numerically assess the validity of
the low Mach number approximation for moist atmospheric flows by contrasting
the low Mach number solution to reference solutions computed with a fully
compressible formulation for a variety of test problems
Low-speed aerodynamic performance of 50.8-centimeter-diameter noise-suppressing inlets for the Quiet, Clean, Short-haul Experimental Engine (QCSEE)
Two basic inlet concepts, a high throat Mach number (0.79) design and a low throat Mach number (0.60) design, were tested with four diffuser acoustical treatment designs that had face sheet porosity ranging from 0 to 24 percent for the high Mach number inlet and 0 to 28 percent for the low Mach number inlet. The tests were conducted in a low speed wind tunnel at free stream velocities of 0, 41, and 62 m/sec and angles of attack to 50 deg. Inlet throat Mach number was varied about the design value. Increasing the inlet diffuser face sheet porosity resulted in an increase in total pressure loss in the boundary layer for both the high and low Mach number inlet designs, however, the overall effect on inlet total pressure recovery of 0.991 at the design throat Mach number, a free stream velocity of 41 m/sec, and an angle of attack of 50 deg; Inlet flow separation at an angle of attack of 50 deg was encountered with only one inlet configuration the high Mach number design with the highest diffuser face sheet porosity (24 percent)
Mach Number Dependence of Electron Heating in High Mach Number Quasiperpendicular Shocks
Efficiency of electron heating through microinstabilities generated in the
transition region of a quasi-perpendicular shock for wide ange of Mach numbers
is investigated by utilizing PIC (Particle-In-Cell) simulation and model
analyses. In the model analyses saturation levels of effective electron
temperature as a result of microinstabilities are estimated from an extended
quasilinear (trapping) analysis for relatively low (high) Mach number shocks.
Here, MTSI (modified two-stream instability) is assumed to become dominant in
low Mach number regime, while BI (Buneman instability) to become dominant in
high Mach number regime, respectively. It is revealed that Mach number
dependence of the effective electron temperature in the MTSI dominant case is
essentially different from that in the BI dominant case. The effective electron
temperature through the MTSI does not depend much on the Mach number, although
that through the BI increases with the Mach number as in the past studies. The
results are confirmed to be consistent with the PIC simulations both in
qualitative and quantitative levels. The model analyses predict that a critical
Mach number above which steep rise of electron heating rate occurs may arise at
the Mach number of a few tens.Comment: 9 pages, 5 figures, Phys. Plasmas in pres
Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces
The local well-posedness and low Mach number limit are considered for the
multi-dimensional isentropic compressible viscous magnetohydrodynamic equations
in critical spaces. First the local well-posedness of solution to the viscous
magnetohydrodynamic equations with large initial data is established. Then the
low Mach number limit is studied for general large data and it is proved that
the solution of the compressible magnetohydrodynamic equations converges to
that of the incompressible magnetohydrodynamic equations as the Mach number
tends to zero. Moreover, the convergence rates are obtained.Comment: 37page
New numerical solver for flows at various Mach numbers
Many problems in stellar astrophysics feature flows at low Mach numbers.
Conventional compressible hydrodynamics schemes frequently used in the field
have been developed for the transonic regime and exhibit excessive numerical
dissipation for these flows. While schemes were proposed that solve
hydrodynamics strictly in the low Mach regime and thus restrict their
applicability, we aim at developing a scheme that correctly operates in a wide
range of Mach numbers. Based on an analysis of the asymptotic behavior of the
Euler equations in the low Mach limit we propose a novel scheme that is able to
maintain a low Mach number flow setup while retaining all effects of
compressibility. This is achieved by a suitable modification of the well-known
Roe solver. Numerical tests demonstrate the capability of this new scheme to
reproduce slow flow structures even in moderate numerical resolution. Our
scheme provides a promising approach to a consistent multidimensional
hydrodynamical treatment of astrophysical low Mach number problems such as
convection, instabilities, and mixing in stellar evolution.Comment: 16 pages, 8 figures, accepted for publication by A&
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