Pressure‐based adaption indicator for compressible euler equations

Dewar, Jeremy; Kurganov, Alexander; Leopold, Maren

doi:10.1002/num.21970

Cited by 10 publications

(8 citation statements)

References 44 publications

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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%

“…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%

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Numerical dissipation switch for two-dimensional central-upwind schemes

2021

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We propose a numerical dissipation switch, which helps to control the amount of numerical dissipation present in central-upwind schemes. Our main goal is to reduce the numerical dissipation without risking oscillations. This goal is achieved with the help of a more accurate estimate of the local propagation speeds in the parts of the computational domain, which are near contact discontinuities and shears. To this end, we introduce a switch parameter, which depends on the distributions of energy in the x- and y-directions. The resulting new central-upwind is tested on a number of numerical examples, which demonstrate the superiority of the proposed method over the original central-upwind scheme.

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Section: Example 5 -Implosionmentioning

confidence: 84%

Section: Example 4 -Explosionmentioning

confidence: 99%

Numerical dissipation switch for two-dimensional central-upwind schemes

2021

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“…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%

Hybrid BSQI-WENO Based Numerical Scheme for Hyperbolic Conservation Laws

Kumar,

Baskar

2018

Preprint

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In this paper, we intend to use a B-spline quasi-interpolation (BSQI) technique to develop higher order hybrid schemes for conservation laws. As a first step, we develop cubic and quintic B-spline quasi-interpolation based numerical methods for hyperbolic conservation laws in 1 space dimension, and show that they achieve the rate of convergence 4 and 6, respectively. Although the BSQI schemes that we develop are shown to be stable, they produce spurious oscillations in the vicinity of shocks, as expected. In order to suppress the oscillations, we conjugate the BSQI schemes with the fifth order weighted essentially non-oscillatory (WENO5) scheme. We use a weak local truncation based estimate to detect the high gradient regions of the numerical solution. We use this information to capture shocks using WENO scheme, whereas the BSQI based scheme is used in the smooth regions. For the time discretization, we consider a strong stability preserving (SSP) Runge-Kutta method of order three. At the end, we demonstrate the accuracy and the efficiency of the proposed schemes over the WENO5 scheme through numerical experiments.

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“…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%

Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator

Chertock¹,

Kurganov²

2023

EAJAM

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We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind numerical fluxes, the three-stage third-order strong stability preserving Runge-Kutta time integrator, and the fifth-order WENO-Z interpolation. The adaptive strategy is implemented by applying the limited interpolation only in the parts of the computational domain where the solution is identified as rough with the help of a smoothness indicator. We develop and use a new simple and robust local smoothness indicator (LSI), which is applied to the solutions computed at each of the three stages of the ODE solver. The new LSI and adaptive A-WENO schemes are tested on the Euler equations of gas dynamics. We implement the proposed LSI using the pressure, which remains smooth at contact discontinuities, while our goal is to detect other rough areas and apply the limited interpolation mostly in the neighborhoods of the shock waves. We demonstrate that the new adaptive schemes are highly accurate, non-oscillatory, and robust. They outperform their fully limited counterparts (the A-WENO schemes with the same numerical fluxes and ODE solver but with the WENO-Z interpolation employed everywhere) while being less computationally expensive.

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Pressure‐based adaption indicator for compressible euler equations

Cited by 10 publications

References 44 publications

Numerical dissipation switch for two-dimensional central-upwind schemes

Numerical dissipation switch for two-dimensional central-upwind schemes

Hybrid BSQI-WENO Based Numerical Scheme for Hyperbolic Conservation Laws

Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator

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