A diffusion-regulated scheme for the compressible Navier–Stokes equations using a boundary-layer sensor

Kalita, Paragmoni; Dass, Anoop K.

doi:10.1016/j.compfluid.2016.02.001

Cited by 4 publications

(5 citation statements)

References 29 publications

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“…This is expected because of the high accuracy of TV-AWS scheme in resolving stationary contact discontinuities. Further, it may be noted that Kalita and Dass (2016) had attributed the higher skin friction profile of the DRLLFV scheme compared with John et al ’s (2014) results, to the higher accuracy of the former because of its controlled numerical diffusion. In conformity with this hypothesis it is observed that the DRvLFV, AUSM and DRAUSMV schemes perform at par with the DRLLFV scheme.…”

Section: Resultsmentioning

confidence: 99%

“…To demonstrate the application of the new methodology to the two schemes, a new scaling function is introduced. The proposed scaling function operates based on a boundary layer sensor (Kalita and Dass, 2016). The boundary layer sensor r vg is the absolute value of the ratio of velocity gradient across the cell interface to that at the wall.…”

Section: The Newly Proposed Methodology Applied On Van Leer’s Fvs and Ausm Schemesmentioning

confidence: 99%

“…For two-dimensional (2D) flows the unsteady Navier–Stokes equations can be written in non-dimensionalized form as: where the conservative variable vector U and the inviscid flux vectors F I and G I are given by: Here e m refers to the total energy of the fluid per unit mass and the rest of the symbols bear their usual meanings. The viscous flux vectors F v and G v are given by: The stress and heat flux terms in the viscous flux vectors are non-dimensionalized as suggested by Kalita and Dass (2016). It is evident that if the viscous fluxes are set to zero and the subscript “I” is dropped from the inviscid flux vectors in equation (1), one obtains the 2D unsteady Euler equations of gas dynamics.…”

Section: Governing Equations and The Discrete Equations On Finite Volume Frameworkmentioning

confidence: 99%

“…At the same time, it should be borne in the mind that excessive numerical diffusion spoils the accuracy by smearing the discontinuities and shear layers, especially in viscous flow computations. Consequently, such computations result in the underprediction of skin friction and wall heat fluxes (van Leer, 1991; Liou and Steffen, 1993; Kalita and Dass, 2016) and overprediction of the separation bubble sizes (Kalita and Dass, 2014) and adiabatic wall temperatures (Kalita et al , 2016). It may further be noted that stability demands relatively high numerical diffusion in zones of shocks or sharp gradients, whereas accuracy calls for minimal numerical diffusion in smooth flow regions including shear layers (Kalita and Dass, 2017).…”

Section: Introductionmentioning

confidence: 99%

“…The application of that function improved the accuracy of a central flux scheme, namely, Diffusion-Regulated Local Lax Friedrichs (DRLLF) scheme (Jaisankar and Raghurama Rao, 2007). The resultant scheme was termed the DRLLF-Viscous (DRLLFV) scheme (Kalita and Dass, 2016). The DRLLFV scheme proved to be more accurate even than the AUSM scheme that is known for its high accuracy in viscous flow computations.…”

Section: Introductionmentioning

confidence: 99%

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A new approach for numerical-diffusion control of flux-vector-splitting schemes for viscous-compressible flows

Kalita

Dass

Hazarika

2020

HFF

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Purpose The flux vector splitting (FVS) schemes are known for their higher resistance to shock instabilities and carbuncle phenomena in high-speed flow computations, which are generally accompanied by relatively large numerical diffusion. However, it is desirable to control the numerical diffusion of FVS schemes inside the boundary layer for improved accuracy in viscous flow computations. This study aims to develop a new methodology for controlling the numerical diffusion of FVS schemes for viscous flow computations with the help of a recently developed boundary layer sensor. Design/methodology/approach The governing equations are solved using a cell-centered finite volume approach and Euler time integration. The gradients in the viscous fluxes are evaluated by applying the Green’s theorem. For the inviscid fluxes, a new approach is introduced, where the original upwind formulation of an FVS scheme is first cast into an equivalent central discretization along with a numerical diffusion term. Subsequently, the numerical diffusion is scaled down by using a novel scaling function that operates based on a boundary layer sensor. The effectiveness of the approach is demonstrated by applying the same on van Leer’s FVS and AUSM schemes. The resulting schemes are named as Diffusion-Regulated van Leer’s FVS-Viscous (DRvLFV) and Diffusion-Regulated AUSM-Viscous (DRAUSMV) schemes. Findings The numerical tests show that the DRvLFV scheme shows significant improvement over its parent scheme in resolving the skin friction and wall heat flux profiles. The DRAUSMV scheme is also found marginally more accurate than its parent scheme. However, stability requirements limit the scaling down of only the numerical diffusion term corresponding to the acoustic part of the AUSM scheme. Originality/value To the best of the authors’ knowledge, this is the first successful attempt to regulate the numerical diffusion of FVS schemes inside boundary layers by applying a novel scaling function to their artificial viscosity forms. The new methodology can reduce the erroneous smearing of boundary layers by FVS schemes in high-speed flow applications.

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Section: Resultsmentioning

confidence: 99%

Section: The Newly Proposed Methodology Applied On Van Leer’s Fvs and Ausm Schemesmentioning

confidence: 99%