Affordable shock-stable item for Godunov-type schemes against carbuncle phenomenon

Chen, Shusheng; Yan, Chao; Lin, Boxi; Liu, Liyuan; Yu, Jian

doi:10.1016/j.jcp.2018.07.022

Cited by 41 publications

(9 citation statements)

References 17 publications

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“…The new formulation significantly improves the resolution of contact wave and, most importantly, is free from carbuncle instability for strong shock. Future work will investigate whether the reduced dissipation across the contact interface also improves the behavior of the HLL solver for the description of viscous flow, often penalized by excessive dissipation across the shear wave 16,20 .…”

Section: Discussionmentioning

confidence: 99%

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: Discussionmentioning

confidence: 99%

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

2019

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“…It is reported that many numerical fluxes fail to produce a stable and symmetry bow shock ahead of a cylinder at hypersonic speeds, particularly when computational cells have a large aspect ratio. [37][38][39] We have conducted such Mach 20 cases 37 with 800 cells in the circumferential direction and 30 cells in the wall-normal direction, covering a fan-shaped space of ±75 degrees upstream the cylinder. First-order accurate methods are employed both in space and time (ie, Euler explicit method), and the computations are run with CFL = 0.5 for 40 000 steps.…”

Section: Appendix F Severe Hypersonic Problemmentioning

confidence: 99%

“…This comes with no surprise, since the proposed methods recover to the original HLLC (which is known to be carbuncle-prone, as well as the Roe flux) at supersonic speeds. These could be remedied by a multidimensional dissipation strategy, 8,37,40,41 and the research in this direction is ongoing. Nevertheless, we have demonstrated that HLLC can be expressed in the AUSM form, and also that it is extendable to all speeds by the same strategy as in the AUSM-family (such as SLAU).…”

Section: Appendix F Severe Hypersonic Problemmentioning

confidence: 99%

AUSM‐like expression of HLLC and its all‐speed extension

Kitamura

Shima

2019

Numerical Methods in Fluids

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Summary Advection upstream splitting method (AUSM) and Harten‐Lax‐van Leer with contact (HLLC) are two popular families of flux functions. The AUSM is simple and requires no eigenstructure, which facilitates its extensions to general equations of state. Furthermore, one of its variants, simple low‐dissipation AUSM (SLAU), is applicable to all speeds and features removal of parameter setting by the user. HLLC, on the other hand, clearly defines three distinct waves in Riemann problem, namely, left‐running and right‐running acoustic waves, and entropy wave. This paper demonstrates that HLLC can be written in a very similar form with the AUSM family and that the similar manner in extending AUSM family to all speeds is easily incorporated into HLLC in this AUSM‐like form. Then, we combine the strengths of the both flux functions and offer a new inviscid numerical flux function within the framework of monotone upwind scheme for conservation laws (MUSCL) in computational fluid dynamics (CFD) for Euler and Navier‐Stokes equations. The resultant HLLC with low dissipation (HLLCL) numerical flux can compute low Mach number flows and sound propagations at the same time with high accuracy, as demonstrated by one‐dimensional and two‐dimensional numerical examples. Furthermore, the results indicate that its extensions to general fluids such as supercritical fluids are encouraging.

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“…In the current study, we call a method with face velocity and face pressure by the expressions ( 37) and (38), or (37) and (39), with the coefficients by the expressions (35) and (36), or simplifications thereof, as a method using characteristic equations, and we denote it by CHAR-CPS-ZB. As an example, we take the recent method by Kitamura and Shima [13], although they call their method as being of HLLC-type (see section 12 on the HLL-method).…”

Section: Determination Of the Face State With Characteristic Equationsmentioning

confidence: 99%

“…A shock unstable HLLCmethod may thus be stabilised by adding shear diffusion. Examples of such methods are those of Shen et al [34], Chen et al [35], and Simon and Mandal [36]. The HLLEM may be stabilised in a similar way.…”

Section: Shock Stabilitymentioning

confidence: 99%