Semiconservative reduced speed of sound technique for low Mach number flows with large density variations

Context. 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 in which density perturbations are much smaller than the background density. In addition, nonconservative variables are required to be evolved using this method, which is not suitable in cases where discontinuities such as shock waves coexist in a single numerical domain. Aims. In this study, we suggest a new semiconservative formulation of the RSST that can be applied to low Mach number flows with large density variations. Methods. 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. Results. 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 semiconservative 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. Conclusions. The newly suggested forms of RSST can be applied to a wider range of low Mach number flows.

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Computation of non-isothermal and compressible low Mach number gas flows by fully explicit scheme using control method for speed of sound

Journal of Advanced Simulation in Science and Engineering ◽

10.15748/jasse.6.11 ◽

2019 ◽

Vol 6 (1) ◽

pp. 11-20

Author(s):

Daisuke Toriu ◽

Satoru Ushijima

Keyword(s):

Mach Number ◽

Speed Of Sound ◽

Control Method ◽

Explicit Scheme ◽

Gas Flows ◽

Low Mach Number

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Shock-less Hypersonic Intakes

10.32920/ryerson.14665317.v1 ◽

2021 ◽

Author(s):

Seyed Hossein Miri

Keyword(s):

Exact Solution ◽

Mach Number ◽

Finite Volume Method ◽

Conical Flow ◽

Low Mach Number ◽

Simulation Based ◽

Line Singularity ◽

Air Intake ◽

Volume Method ◽

Intake Flow

The accuracy of CFD for simulating hypersonic air intake flow is verified by calculating the flow inside a Busemann type intake. The CFD results are then compared against the “exact” solution for the Busemann intake as calculated from the Taylor-McColl equations for conical flow. The method proposed by G. Emanuel (the Lens Analogy) for generating an intake shape that transforms parallel and uniform hypersonic (freestream) flow isentropically to another parallel and uniform, less hypersonic, flow has been verified by CFD (SOLVER II) simulation, based on Finite Volume Method (FVM). The shock-less (isentropic) nature of the Lens Analogy (LA) flow shapes has been explored at both on and off-design Mach numbers. The Lens Analogy (LA) method exhibits a limit line (singularity) for low Mach number flows, where the streamlines perform an unrealistic reversal in direction. CFD calculations show no corresponding anomalies.

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Projection method for high-order compact schemes for low Mach number flows in enclosures

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-07-2012-0167 ◽

2014 ◽

Vol 24 (5) ◽

pp. 1141-1174 ◽

Cited By ~ 5

Author(s):

Artur Tyliszczak

Keyword(s):

Mach Number ◽

Boundary Conditions ◽

Projection Method ◽

High Order ◽

Staggered Grid ◽

Constant Density ◽

Computational Domain ◽

Content Type ◽

Low Mach Number ◽

Large Density

Purpose – Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low Mach number flows with large density and temperature variations. Design/methodology/approach – Low Mach number approximation approach is used in the paper combined with a predictor-corrector method and accurate compact scheme of fourth and sixth order. A novel algorithm is formulated for the projection method in which the boundary conditions for the pressure are implemented in such a way that the continuity equation is fulfilled everywhere in the computational domain, including the boundary nodes. Findings – It is shown that proposed implementation of the boundary conditions considerably improves a solution accuracy. Assessment of the accuracy was performed based on the constant density Burggraf flow and for two benchmark cases for the natural convection problems: steady flow in a square cavity and unsteady flow in a tall cavity. In all the cases the results agree very well with exemplary solutions. Originality/value – A staggered or half-staggered grid arrangement is usually used for the projection method for both constant and low Mach number flows. The staggered approach ensures stability and strong pressure-velocity coupling. In the paper a high-order compact method has been implemented in the framework of low Mach number approximation on collocated meshes. The resulting algorithm is accurate, robust for large density variations and is almost free from the pressure oscillations.

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