2015
DOI: 10.1002/num.21970
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Pressure‐based adaption indicator for compressible euler equations

Abstract: We consider the Euler equations of gas dynamics and develop a new adaption indicator, which is based on the weak local residual measured for the nonconservative pressure variable. We demonstrate that the proposed indicator is capable of automatically detecting discontinuities and distinguishing between the shock and contact waves when they are isolated from each other. We then use the developed indicator to design a scheme adaption algorithm, according to which nonlinear limiters are used only in the vicinity … Show more

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Cited by 13 publications
(8 citation statements)
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“…As demonstrated in [38] (also see [7,26]), a jet of fluid is expected to emerge. However, the numerical diffusion may prevent the jet from appearing in the computed results or may artificially slow down its propagation speed.…”
Section: Example 5 -Implosionmentioning
confidence: 84%
See 1 more Smart Citation
“…As demonstrated in [38] (also see [7,26]), a jet of fluid is expected to emerge. However, the numerical diffusion may prevent the jet from appearing in the computed results or may artificially slow down its propagation speed.…”
Section: Example 5 -Implosionmentioning
confidence: 84%
“…The computational domain is [0, 1.5] × [0, 1.5]. It is well-known (see, e.g., [7,21,26,38]) that the computed circular contact curve should develop instability by the time = 3.2 unless the numerical method contains an excessive amount of numerical dissipation. Therefore, this is a good test to compare the numerical dissipation present in the NEW and OLD schemes.…”
Section: Example 4 -Explosionmentioning
confidence: 99%
“…We extend the Hybrid6 scheme for system of equations in component-wise manner. In order to make the algorithm more efficient, Dewar et al [8] used only the WLTE of pressure term. This can be following in our case as well, but we use the WLTE for each equation separately.…”
Section: Example 7 (Non-convex Flux -Buckley-leverett Equation)mentioning
confidence: 99%
“…In [22,23], the edges in the computed solution were detected using its Fourier coefficient. One can also identify the rough parts of the computed solution using the numerical production of entropy (see, e.g., [48,49]), the entropy residual (see, e.g., [26,27]), or the weak local residual (see, e.g., [15,33,34]).…”
Section: Introductionmentioning
confidence: 99%