The momentum interpolation method based on the time-marching algorithm for All-Speed flows

a b s t r a c tLow Mach number flow computation in co-located grid arrangement requires pressurevelocity coupling in order to prevent the checkerboard phenomenon. Two broad categories of pressure-velocity coupling methods for unsteady flows can be distinguished based on the time-step dependency of the coupling coefficient in the definition of the transporting velocity on a face of a control volume. As an example of the time-step independent category, the AUSM + -up scheme is studied. As an example of the second category, Rhie-Chow momentum interpolation methods are studied. Within the momentum interpolation techniques, again two broad categories can be distinguished based on the time-step dependency of the coupling coefficient used for unsteady flow computations, but when a steady state is reached. Variants of Rhie-Chow interpolation methods in each subcategory are studied on critical test cases. The result of the study is that for a good representation of unsteady flows containing acoustic information, the pressure-velocity coupling coefficient must explicitly depend on the time-step, but that the transporting velocity must become independent of the time-step when a steady state is reached.

show abstract

“…[6,11,20], but not for the ones suggested in Refs. [2,5,15]. Let us emphasize that, as clearly shown in Ref.…”

Section: Introductionmentioning

confidence: 59%

“…In the second class, the pressure-velocity coupling is explicitly time-step dependent in unsteady calculation (see e.g. [2,5,6,11,15,20]). Rhie-Chow interpolation, which consists in the construction of the transporting -or interface -velocity inspired by the method presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

Pressure–velocity coupling allowing acoustic calculation in low Mach number flow

Moguen¹,

Kousksou²,

Bruel³

et al. 2012

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…On the basis of the key idea of MIM, Ref. [18] derived the time-marching MIM, in which a two-dimensional steady form can be expressed as follows: 1 1 2 1 2 11…”

Section: Analysis Of the Mim Role In Shock And Improvementmentioning

confidence: 99%

Role of the momentum interpolation mechanism of the Roe scheme in shock instability

Ren

2016

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

Summary The shock instability phenomenon is a well‐known problem for hypersonic flow computation by the shock‐capturing Roe scheme. The pressure checkerboard is another well‐known problem for low‐Mach‐number flow computation. The momentum interpolation method (MIM) is necessary for low‐Mach‐number flows to suppress the pressure checkerboard problem, and the pressure‐difference‐driven modification for cell face velocity can be regarded as a version of the MIM by subdividing the numerical dissipation of the Roe scheme. In this paper, MIM has been discovered through analysis and numerical tests to have the most important function in shock instability. MIM should be completely removed for nonlinear flows. However, the unexpected MIM is activated on the cell face nearly parallel to the flow for the high‐Mach‐number flows or low‐Mach‐number cells in numerical shock. Therefore, MIM should be retained for low‐Mach‐number flows and be completely removed for high‐Mach‐number flows and low‐Mach‐number cells in numerical shock. For such conditions, two coefficients are designed on the basis of the local Mach number and a shock detector. Thereafter, the improved Roe scheme is proposed. This scheme considers the requirement of MIM for incompressible and compressible flows, and is validated for good performance of numerical tests. An acceptable result can also be obtained with only the Mach number coefficient for general practical computation. Therefore, the objective of decreasing rather than increasing numerical dissipation to cure shock instability can be achieved with simple modification. Moreover, the mechanism of shock instability has been profoundly understood, in which MIM plays the most important role, although it is not the only factor. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

“…Through mathematical transformation and asymptotic analysis, Li indicated that the coefficient of the term U L -U R in the momentum equation should be of the order O(a 0 ) or less to control the numerical dissipation and to achieve high resolution at low speeds [18]. Obviously, eq.…”

Section: Construction Of the Pressure Fluxmentioning

confidence: 99%

A parameter-free upwind scheme for all speeds’ simulations

Yan

Sun

et al. 2015

Sci. China Technol. Sci.

View full text Add to dashboard Cite

With the rapid development of the computational fluid dynamics (CFD), a parameter-free upwind scheme capable of simulating all speeds accurately and efficiently is in high demand. To achieve this goal, we present a new upwind scheme called AUSMPWM in this paper. This scheme computes the numerical mass flux as the AUSMPW+ and computes the interfacial sound speed in a different way. Also, it computes the pressure flux by limiting the dissipation if the Mach number is less than 1. Series of numerical experiments show that AUSMPWM can satisfy the following attractive properties independent of any tuning coefficient: (1) Robustness against the shock anomaly and high discontinuity's resolution; (2) high accuracy on hypersonic heating prediction and capability to give smooth reproductions of heating profiles; (3) low dissipation at low speeds; and (4) strong grid, reconstruction scheme, and Mach number independence in low speeds' simulations. These properties suggest that AUSMPWM is promising to be widely used to accurately and efficiently simulate flows of all speeds. shock anomaly, AUSMPW+, ausmpwm, all speeds, computational fluid dynamics Citation: Qu F, Yan C, Sun D, et al. A parameter-free upwind scheme for all speeds' simulations. Sci China Tech Sci,

show abstract

The momentum interpolation method based on the time-marching algorithm for All-Speed flows

Cited by 33 publications

References 27 publications

Pressure–velocity coupling allowing acoustic calculation in low Mach number flow

Pressure–velocity coupling allowing acoustic calculation in low Mach number flow

Role of the momentum interpolation mechanism of the Roe scheme in shock instability

A parameter-free upwind scheme for all speeds’ simulations

Contact Info

Product

Resources

About