Parameter-Free Simple Low-Dissipation AUSM-Family Scheme for All Speeds
01 Aug 2011-AIAA Journal (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 49, Iss: 8, pp 1693-1709
TL;DR: In this paper, a simple low-dissipation numerical flux function of the AUSM-family for all speeds, called the simple low dissipation AUSMs, was proposed.
Abstract: This paper presents a new, simple low-dissipation numerical flux function of the AUSM-family for all speeds, called the simple low-dissipation AUSM. In contrast with existing all-speed schemes, the simple low-dissipation AUSM features low dissipation without any tunable parameters in a low Mach number regime while it keeps the robustness of the AUSM-family fluxes against shock-induced anomalies at high Mach numbers (e.g., carbuncle phenomena). Furthermore, the simple low-dissipation AUSM has a simpler formulation than the other all-speed schemes. These advantages of the present scheme are demonstrated in numerical examples of a wide spectrum of Mach numbers.
Citations
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TL;DR: Three schemes are developed that have Mach-proportional dissipation inside the numerical shock wave structure, in contrast to Mach independent dissipation provided by conventional AUSM fluxes, and their desired performances are demonstrated for a wide spectrum of Mach numbers.
190 citations
Cites background or methods from "Parameter-Free Simple Low-Dissipati..."
...1 SLAU SLAU scheme developed by Shima and Kitamura [25], one of AUSM-family schemes, is briefly explained first....
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...SLAU showed an excellent performance at low speeds [25, 26], not to mention in moderate speed regimes; but as in other flux functions, anomalous behaviors were observed at shocks under some circumstances in hypersonic flows....
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...Inviscid numerical fluxes at cell-interfaces Fi,j (denoted also as F1/2 hereafter) are calculated by one of the following AUSM-family fluxes [13, 25, 31]....
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...The c1/2 is the speed of sound numerically defined at a cell-interface, and usually used to calculate an AUSM-family numerical flux [13, 24, 25] (see Figure 3)....
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...In addition, we remind that SLAU [25], SLAU2, AUSM-up and LDFSS2001 are all-speed schemes that satisfy C) Low dissipation at low speeds Thus, the new schemes are also supposed to have C)....
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TL;DR: In this paper, a new weighted compact nonlinear scheme (WCNS) is presented, where the linear difference scheme is modified to use the flux on the computational nodes together with that on the midpoints.
93 citations
TL;DR: This study proposes a robust and (second-order) accurate hybrid reconstruction method of WLSQ and G–G that is suitable for, but not limited to, those mixed grids in a unified manner, which overcomes the abovementioned difficulties encountered by existing methods.
Abstract: T HE gradient calculation for the reconstruction of dependent variables is one of the critical issues for the accuracy and robustness of computational fluid dynamics (CFD) methods. There are many choices for the reconstruction for arbitrary polyhedra or polygons in unstructured meshes [1–4], which are represented by a family of weighted-least-squares (WLSQ) methods (including unweighted-least-squares [LSQ]) and a Green–Gauss (G–G) method. The WLSQ methods give exact gradients for a linear distribution of thevariables.On the other hand, theG–Greconstruction has this property only on symmetric and uniform meshes, because this method requires variables to be exactly on face centers, which are not generally obtained in a simple manner on Cartesian grids having hanging nodes (Fig. 1), for instance. Meanwhile, on thin-and-curved mesh that often appears in boundary layers for highReynolds number flow simulations, LSQ reportedly gives totally erratic gradients [1]; WLSQwith a properly chosen weighting function or G–G has better performance, albeit associated with certain errors, as shown in [5]. Therefore, each cell type/geometry has its own favorite gradient reconstructionmethods, for example Cartesian grids preferWLSQ to G–G, whereas thin-and-curved mesh does the opposite. Then, it is a natural question how to deal with the mixed grids of different types of cells. In recent years, body-fitted/Cartesian hybrid grids (sometimes called viscous Cartesian grids) [4,6–9] have been recognized as one of the standard types of unstructured grids, because they can resolve boundary layers as well as structured grids do, while saving the number of cells away from the wall. Thus, in this study, we will propose a robust and (second-order) accurate hybrid reconstruction method of WLSQ and G–G that is suitable for, but not limited to, those mixed grids in a unified manner, which overcomes the abovementioned difficulties encountered by existing methods. Our discussions are based on cell-centered schemes but are extendable to the cell-vertex counterpart by the simple replacement of the word “cell” with “control volume.” We point out here that many CFD practitioners still desire secondorder accuracy in space within the framework of an unstructured grid finite volume method (FVM) [10–13]. This has motivated us to pursue a second-order-accurate reconstruction method that is applicable to wide-ranging grid types and/or geometries, in spite of the growing attention to more sophisticated, higher order methods, such as in [14], spectral volume [15], or residual distribution [16,17] in the past several years.
90 citations
Cites methods from "Parameter-Free Simple Low-Dissipati..."
...” The inviscid flux can be computed by any numerical flux functions such as an approximate Riemann problem solver, and we chose an advection upstream splitting method (AUSM)-type scheme, simple low-dissipation AUSM (SLAU) [18] here, using physical quantities on both sides of the cell interface and face normal of the cell interface....
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...G-G, WLSQ (0), and GLSQ (without a slope limiter) are used to calculate gradients, and SLAU [18] is used as a numerical flux function....
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...The inviscid flux can be computed by any numerical flux functions such as an approximate Riemann problem solver, and we chose an advection upstream splitting method (AUSM)-type scheme, simple low-dissipation AUSM (SLAU) [18] here, using physical quantities on both sides of the cell interface and face normal of the cell interface....
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TL;DR: In this article, the authors explored the reasons for the non-physical behavior, checkerboard and global cut-off problems of the preconditioned and all-speed Roe-type schemes.
80 citations
TL;DR: In this article, an improved immersed boundary method for turbulent flow simulation on Cartesian grids is proposed to determine the appropriate boundary conditions, near-wall approximation of the mean-flow equatio...
Abstract: An improved immersed boundary method for turbulent flow simulation on Cartesian grids is proposed. To determine the appropriate boundary conditions, near-wall approximation of the mean-flow equatio...
65 citations
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TL;DR: AUSM+ as discussed by the authors improves the AUSM by exact resolution of 1D contact and shock discontinuities, positivity preserving of scalar quantity such as the density, free of the carbuncle phenomenon, and free of oscillations at the slowly moving shock.
986 citations