Capturing Shock Reflections: An Improved Flux Formula

Donat, Rosa; Marquina, Antonio

doi:10.1006/jcph.1996.0078

Cited by 253 publications

(254 citation statements)

References 20 publications

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“…This strategy has been used in flux-vector splitting and characteristic-based methods (see [3,24,11]). The flux Jacobian matrix is quite important to any characteristic-based method and in many real gas computations, since it determines the transformation to characteristic fields and thus the local propagation of independent waves, as well as what quantities are to be upwind differenced.…”

Section: The First-order Methodsmentioning

confidence: 99%

“…The flux Jacobian matrix is quite important to any characteristic-based method and in many real gas computations, since it determines the transformation to characteristic fields and thus the local propagation of independent waves, as well as what quantities are to be upwind differenced. Near an unresolved step gradient in the flow, in which the states Q L and Q R vary by a large amount from one node to the next, we use the two flux Jacobian matrices evaluated at these physical states in an upwind fashion rather than some artificial average, such as the Roe mean [18] or linear average, since the use of a single representative Jacobian seems to produce spurious oscillations in some circumstances (see [3]). …”

Section: The First-order Methodsmentioning

confidence: 99%

“…clarify to smooth out the density with the number of time steps to similar levels, seen for example in Marquina's scheme [3] or the HLL scheme [24]. This means that our scheme has built-in heat conduction (see [3]). The third-order scheme has less dissipation for stationary-contact discontinuity.…”

Section: One-dimensional Testsmentioning

confidence: 97%

“…The gas is thus compressed and heated, giving rise to a shock which propagates off the wall. The "overheating effects" occur in the first few zones near the wall [15,3], when the shock reflects off the stationary solid wall. Following Noh [15], a numerical scheme with a built-in heat conduction mechanism will be able to dissipate the overheating.…”

Section: One-dimensional Testsmentioning

confidence: 99%

“…We use the numerical treatment of [27,3,23] near the corner to fix the errors generated: a boundary layer in density of about one to two zones, the decrease of the two components of the velocity, as well as a spurious Mach steam at the bottom wall (see [23] for corner treatment using equilibrium equations of state).…”

Section: Two-dimensional Testsmentioning

confidence: 99%

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A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

Stiriba¹

2002

Journal of Computational Physics

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We present and analyze the performance of a nonlinear, upwind flux split method for approximating solutions of hyperbolic conservation laws. The method is based on a new version of the single-state-approximate Riemann solver devised by Harten, Lax, and van Leer (HLL) and implemented by Einfeldt. It makes use of two-sided local characteristic variables to reduce the dissipation of HLL by introducing the flavor of HLL into the Steger-Warming flux vector splitting scheme. We use the characteristic decomposition and the method-of-lines approach to construct high-order versions of the first-order scheme and demonstrate their efficiency and robustness in several numerical tests.

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Section: The First-order Methodsmentioning

confidence: 99%

Section: The First-order Methodsmentioning

confidence: 99%

Section: One-dimensional Testsmentioning

confidence: 97%

Section: One-dimensional Testsmentioning

confidence: 99%

Section: Two-dimensional Testsmentioning

confidence: 99%

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A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

Stiriba¹

2002

Journal of Computational Physics

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Numerical Fluid Modelling of the Plasma Edge Response to a 3D Object and Application to Mach Probe Measurements

Paredes

Serre

Schwander

et al. 2014

Contrib. Plasma Phys.

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The penalization method Ref. [1] is used to model the interaction of 3D probe with an isothermal plasma. Density maps show that the region perturbed by the obstacle, is not restricted to its near neighbourhood, but can extend to the whole SOL. In the particular case of a probe, which is used to measure local plasma parameters, this impact can lead to violation of assumptions of locality of the perturbation usually used in determining Mach number from the imbalance in density on both sides of the probe. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Adaptive mesh refinement techniques for high‐order shock capturing schemes for multi‐dimensional hydrodynamic simulations

Baeza

Mulet

2006

Numerical Methods in Fluids

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SUMMARYThe numerical simulation of physical phenomena represented by non-linear hyperbolic systems of conservation laws presents speciÿc di culties mainly due to the presence of discontinuities in the solution. State of the art methods for the solution of such equations involve high resolution shock capturing schemes, which are able to produce sharp proÿles at the discontinuities and high accuracy in smooth regions, together with some kind of grid adaption, which reduces the computational cost by using ÿner grids near the discontinuities and coarser grids in smooth regions. The combination of both techniques presents intrinsic numerical and programming di culties. In this work we present a method obtained by the combination of a high-order shock capturing scheme, built from Shu-Osher's conservative formulation (J. Comput. Phys. 1988; 77:439-471; 83:32-78), a ÿfth-order weighted essentially non-oscillatory (WENO) interpolatory technique (J. Comput. Phys. 1996; 126:202-228) and Donat-Marquina's ux-splitting method (J. Comput. Phys. 1996; 125:42-58), with the adaptive mesh reÿnement (AMR) technique of Berger and collaborators (Adaptive mesh reÿnement for hyperbolic partial di erential equations.

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Capturing Shock Reflections: An Improved Flux Formula

Cited by 253 publications

References 20 publications

A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

Numerical Fluid Modelling of the Plasma Edge Response to a 3D Object and Application to Mach Probe Measurements

Adaptive mesh refinement techniques for high‐order shock capturing schemes for multi‐dimensional hydrodynamic simulations

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