Adiabatic shock capturing in perfect gas hypersonic flows

Kirk, Benjamin S.

doi:10.1002/fld.2195

Cited by 8 publications

(10 citation statements)

References 21 publications

(35 reference statements)

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“…Kirk showed how this shock‐capturing term is capable of recovering practically the right preshock total‐enthalpy level for supersonic/hypersonic inviscid flow fields, in accordance with the physical behavior expected.…”

Section: Rd Schemes For the Navier‐stokes Equationssupporting

confidence: 71%

“…In this contribution, we have exploited the shock‐capturing term in combination with the multidimensional upwind L D A RD scheme. However, nothing in the formulation employed prevents to combine the shock‐capturing term in combination with other RD schemes, or with FV , stabilized finite element, or DG schemes.…”

Section: Discussionmentioning

confidence: 99%

“…This expression makes evident how the first term

{\overset{Φ}{true}}_{l}^{c, Ω_{i}, L D A}

addresses the advection of smooth information, whereas the second term, locally active (ie, modulated by the shock detector), provides additional dissipation to handle strong gradients. In this sense, the B x scheme in Equation can be seen as a stabilized finite element scheme supplemented with a shock‐capturing term …”

Section: Rd Schemes For the Navier‐stokes Equationsmentioning

confidence: 99%

“…The discretized shock‐capturing term corresponding to

{\overset{W}{true}}_{2} \equiv {\overset{U}{true}}^{H}

is given by

{\overset{δ}{true}}_{l}^{H} = \sum_{Ω_{i} \in Ξ_{l}} \int_{Ω_{i}} μ^{a r t} \nabla N_{l} \frac{\partial {\overset{U}{true}}^{H}}{\partial \overset{U}{true}} \nabla \overset{U}{true} d v .

…”

Section: Rd Schemes For the Navier‐stokes Equationsmentioning

confidence: 99%

“…Moreover, the aforementioned principle applies as well to systems of advection-diffusion equations, eg, the compressible Navier-Stokes equations. Indeed, many different numerical techniques exploiting this principle have been proposed in the literature; one can find numerical methods based on finite difference (FD), 5,6 finite volume (FV), [7][8][9] streamline upwind Petrov-Galerkin finite element (FE [10][11][12], and discontinuous Galerkin (DG 13,14 ) discretization.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An enthalpy‐preserving shock‐capturing term for residual distribution schemes

Garicano‐Mena

Degrez

2018

Numerical Methods in Fluids

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Summary In this contribution, we investigate strategies to perform shock‐capturing computation of steady hypersonic flow fields by means of residual distribution schemes. The ultimate objective is the computation of flow solutions for which the correct upstream enthalpy value is recovered in the postshock region. To this end, the parallelism existing between the classical Bx scheme and the stabilized finite element techniques is exploited. The simple Lax‐Friedrichs dissipation term is leveraged to build two new residual distribution schemes. Upon testing on both inviscid and viscous steady problems, solutions obtained with one of the two schemes are shown to recover the correct upstream total enthalpy level in the postshock region. This last scheme provides also improved wall pressure and skin friction predictions; heat transfer predictions are, unfortunately, similar to those offered by the Bx scheme. A conjecture for explaining this behavior is exposed.

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Section: Rd Schemes For the Navier‐stokes Equationssupporting

confidence: 71%

Section: Discussionmentioning

confidence: 99%

“…This expression makes evident how the first term