A Hybrid Numerical Method to Cure Numerical Shock Instability

Wu, Hao; Shen, Longjun; Shen, Zhijun

doi:10.4208/cicp.041009.270410a

Cited by 25 publications

(15 citation statements)

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“…It is suggested that using a dissipative scheme in shock region while a less dissipative one elsewhere may tackle this problem. From then, several successful approaches 10, [14][15][16] have been proposed by relying on hybridization. However, the choice and design of switching parameters required in the hybrid methods usually have some arbitrariness.…”

Section: Introductionmentioning

confidence: 99%

“…This arbitrariness in parameters may lead to failures for complex flow cases 17 . Moreover, the hybridization of complementary solvers may break the strict Rankine-Hugoniot jump conditions, which will result in smearing contact discontinuities 15 . Realizing the drawbacks of hybrid methods, other ideas have been tried to modify the HLL-type approximate Riemann solver.…”

Section: Introductionmentioning

confidence: 99%

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A new formulation for two-wave Riemann solver accurate at contact interfaces

2019

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This study proposes a new formulation for Harten, Lax and van Leer (HLL) type Riemann solver which is capable of solving contact discontinuities accurately but with robustness for strong shock. It is well known that the original HLL, which has incomplete wave structures, is too dissipative to capture contact discontinuities accurately. On the other side, contact-capturing approximate Riemann solvers such as Harten, Lax and van Leer with Contact (HLLC) usually suffer from spurious solutions, also called carbuncle phenomenon, for strong shock. In this work a new accurate and robust HLL-type formulation, so-called HLL-BVD (HLL Riemann solver with BVD) is proposed by modifying the original HLL with BVD (boundary variation diminshing) algorithm. Instead of explicitly recovering the complete wave structures like the way of HLLC, the proposed method restores the missing contact with a jump-like function. The capability of solving contact discontinuities is further improved by minimizing the inherent dissipation term in HLL. Without modifying the original incomplete wave structures of HLL, the robustness for strong shock has been reserved. Thus the proposed method is free from shock instability problem. The accuracy and robustness of the new method are demonstrated through solving several one-and two-dimensional tests. Results indicate that the new formulation based on two-wave HLL-type Riemann solver is not only capable of capturing contact waves more accurately than the original HLL or HLLC but, most importantly, is free form carbuncle instability for strong shock.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new formulation for two-wave Riemann solver accurate at contact interfaces

2019

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“…He recommends using a scheme that does not introduce pressure terms into massflux discretization to ensure shock stability. Wu et al [27] hybridizes both the mass and interface-normal flux component to achieve shock stability. Shen et al [19] on the other hand recommends hybridizing only the interfacenormal flux component on interfaces that are orthogonal to the shock front to avoid shock instability while Zhang et al [31] employs hybridization only on the momentum components.…”

Section: Introductionmentioning

confidence: 99%

A cure for numerical shock instability in HLLC Riemann solver using antidiffusion control

Simon

Mandal

2018

Computers & Fluids

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Various forms of numerical shock instabilities are known to plague many contact and shear preserving approximate Riemann solvers, including the popular Harten-Lax-van Leer with Contact (HLLC) scheme, during high speed flow simulations. In this paper we propose a simple and inexpensive novel strategy to prevent the HLLC scheme from developing such spurious solutions without compromising on its linear wave resolution ability. The cure is primarily based on a reinterpretation of the HLLC scheme as a combination of its well-known diffusive counterpart, the HLL scheme, and an antidiffusive term responsible for its accuracy on linear wavefields. In our study, a linear analysis of this alternate form indicates that shock instability in the HLLC scheme could be triggered due to the unwanted activation of the antidiffusive terms of its mass and interface-normal flux components on interfaces that are not aligned with the shock front. This inadvertent activation results in weakening of the favourable dissipation provided by its inherent HLL scheme and causes unphysical mass flux variations along the shock front. To mitigate this, we propose a modified HLLC scheme that employs a simple differentiable pressure based multidimensional shock sensor to achieve smooth control of these critical antidiffusive terms near shocks. Using a linear perturbation analysis and a matrix based stability analysis, we establish that the resulting scheme, called HLLC-ADC (Anti-Diffusion Control), is shock stable over a wide range of freestream Mach numbers. Results from standard numerical test cases demonstrate that the HLLC-ADC scheme is indeed free from the most common manifestations of shock instability including the Carbuncle phenomenon without significant loss of accuracy on shear dominated viscous flows.

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“…For example, Quirk 7 suggested replacing the low‐dissipative scheme with a high‐dissipative scheme, for example, HLLE scheme, in the vicinity of a strong shock. Wu et al 25 presented the hybrid scheme to cure the numerical shock instability of the Roe scheme by blending it with the HLL scheme. They concluded that the phenomenon was related to insufficient dissipation of the contact and shear surfaces.…”

Section: Introductionmentioning

confidence: 99%

A stable hybrid Roe scheme on triangular grids

Phongthanapanich

2020

Numerical Methods in Fluids

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Numerical shock instability is a common problem for shock‐capturing methods that try to resolve contact and shear waves with minimal diffusion. Most flux‐difference splitting and the AUSM family of schemes produce the carbuncle phenomenon on both structured and unstructured grids. The original Roe scheme is well known to generate shock anomalies and can lead to nonentropic weak solutions to the Euler equations. A simple and robust approach for healing these numerical instabilities is to apply the hybrid technique incorporated with an efficient weighting switch function to control the amount of dissipation in the vicinity of shock waves. This article proposes a simple, robust, and accurate hybrid Roe scheme (Roe+ scheme) by hybridizing the Roe scheme and the modified AUSMV+ scheme. A new normalized pressure/density‐based weighting switch function is proposed and applied to the scheme to minimize the numerical dissipation and maintain the robustness of the hybridization. The linearized discrete analysis is performed to evaluate the proposed scheme according to the perturbation damping mechanism of an odd–even decoupling problem. The resulting recursive equations indicate that the hybridized mechanism damps all perturbations effectively. Finally, several numerical examples demonstrated that the Roe+ scheme provides an accurate, robust, and carbuncle‐free solution on both structured and unstructured triangular grids.

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A Hybrid Numerical Method to Cure Numerical Shock Instability

Cited by 25 publications

References 0 publications

A new formulation for two-wave Riemann solver accurate at contact interfaces

A new formulation for two-wave Riemann solver accurate at contact interfaces

A cure for numerical shock instability in HLLC Riemann solver using antidiffusion control

A stable hybrid Roe scheme on triangular grids

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