skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A new flux splitting scheme for Euler equations of gas dynamics

Abstract

A new flux splitting method named K-CUSP scheme is proposed in the paper. The major difference between K-CUSP and two traditional CUSP schemes (H-CUSP and E-CUSP) is that all kinematic quantities and all thermodynamic quantities in total enthalpy will be separately split into convective term and pressure term. The present scheme adopts the cell-face Mach number splitting method of AUSM+ scheme and the interface flux of pressure term is given a new way in the subsonic regime. Numerical solutions demonstrate that the new scheme inherits the simplicity and robustness of FVS schemes, which overcomes the shortcomings of pressure overshoot of shock wave in H-CUSP and E-CUSP schemes, but also retains the high-resolution of FDS schemes, which achieves the high accuracy of contact discontinuity and shock discontinuity.

Authors:
; ;  [1]
  1. State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)
Publication Date:
OSTI Identifier:
22391176
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1648; Journal Issue: 1; Conference: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ENTHALPY; INTERFACES; MACH NUMBER; NUMERICAL SOLUTION; PRESSURE DEPENDENCE; RESOLUTION; SHOCK WAVES; THERMODYNAMICS

Citation Formats

Li, Xindong, Hu, Zongmin, and Jiang, Zonglin. A new flux splitting scheme for Euler equations of gas dynamics. United States: N. p., 2015. Web. doi:10.1063/1.4913160.
Li, Xindong, Hu, Zongmin, & Jiang, Zonglin. A new flux splitting scheme for Euler equations of gas dynamics. United States. doi:10.1063/1.4913160.
Li, Xindong, Hu, Zongmin, and Jiang, Zonglin. Tue . "A new flux splitting scheme for Euler equations of gas dynamics". United States. doi:10.1063/1.4913160.
@article{osti_22391176,
title = {A new flux splitting scheme for Euler equations of gas dynamics},
author = {Li, Xindong and Hu, Zongmin and Jiang, Zonglin},
abstractNote = {A new flux splitting method named K-CUSP scheme is proposed in the paper. The major difference between K-CUSP and two traditional CUSP schemes (H-CUSP and E-CUSP) is that all kinematic quantities and all thermodynamic quantities in total enthalpy will be separately split into convective term and pressure term. The present scheme adopts the cell-face Mach number splitting method of AUSM+ scheme and the interface flux of pressure term is given a new way in the subsonic regime. Numerical solutions demonstrate that the new scheme inherits the simplicity and robustness of FVS schemes, which overcomes the shortcomings of pressure overshoot of shock wave in H-CUSP and E-CUSP schemes, but also retains the high-resolution of FDS schemes, which achieves the high accuracy of contact discontinuity and shock discontinuity.},
doi = {10.1063/1.4913160},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1648,
place = {United States},
year = {Tue Mar 10 00:00:00 EDT 2015},
month = {Tue Mar 10 00:00:00 EDT 2015}
}
  • A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals, and in some cases surpasses, that of Roe`s solver in the Euler and Navier-Stokes solutions carried out in this study. The scheme is robust and converges as fast as the Roe splitting. We propose an appropriately defined cell-face advection Mach number using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as the advection upstream splitting method (AUSM).more » We also introduce a new pressure splitting which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids. 19 refs., 17 figs.« less
  • The paper describes the development and application of a new Euler solver for adaptive tetrahedral grids. Spatial discretization uses a finite-volume, node-based scheme that is of central-differencing type. A second-order Taylor series expansion is employed to march the solution in time according to the Lax-Wendroff approach. Special upwind-like smoothing operators for unstructured grids are developed for shock-capturing, as well as for suppression of solution oscillations. The scheme is formulated so that all operations are edge-based, which reduces the computational effort significantly. An adaptive grid algorithm is employed in order to resolve local flow features. This is achieved by dividing themore » tetrahedral cells locally, guided by a flow feature detection algorithm. Application cases include transonic flow around the ONERA M6 wing and transonic flow past a transport aircraft configuration. Comparisons with experimental data evaluate accuracy of the developed adaptive solver. 31 refs., 33 figs.« less
  • We investigate the performance of the multiresolution method. The method was recently proposed as a way to speed up computations of compressible flows. The method is based on truncating wavelet coefficients. The method showed good performance on one-dimensional test problems. We implement the method in two space dimensions for a more complex compressible flow computation, intended to simulate conditions under which many production CFD codes are running. Our conclusion is that we can in many cases reduce the CPU time, but that the gain in efficiency is not as large as for the one-dimensional problems. We furthermore observe that itmore » is essential to use the adaptive multiresolution method, which mixes centered differences with TVD methods. 5 refs., 14 figs., 1 tab.« less
  • We derive high-order finite difference schemes for the compressible Euler (and Navier-Stokes equations) that satisfy a semidiscrete energy estimate and present and efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semidiscrete energy estimates is based on symmetrization of the equations, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration-by-parts procedure used in the continuous energy estimate. For the Euler equations, the symmetrization is designed such as to preserve the homogeneity of the flux vectors. Around discontinuities or sharpmore » gradients, refined grids are created on which the discrete equations are solved after adding artificial viscosity. The positioning of the subgrids and computation of the viscosity are aided by a detection algorithm which is based on a multiscale wavelet analysis of the pressure grid function. The wavelet theory provides easy-to-implement mathematical criteria to detect discontinuities, sharp gradients, and spurious oscillations quickly and efficiently. As the detection algorithm does not depend on the numerical method used, it is of general interest. The numerical method described and the detection algorithm are part of a general solution strategy for fluid flows, which is currently being developed by the authors and collaborators. 29 refs., 7 figs., 2 tabs.« less
  • A new kinetic scheme based on the equilibrium flux method (EFM) and modified using Osher intermediate states is proposed. This new scheme called EFMO combines the robustness of the equilibrium flux method and the accuracy of flux-difference splitting schemes. The original EFM scheme is expressed in terms of simple wave decomposition in which only the linearly degenerate subpath is calculated from Osher numerical flux while nonlinear waves are still evaluated from the regular EFM splitting. Owing to its capability of withstanding intense nonlinear waves and yet exactly resolving contact discontinuities, EFMO is particularly well suited for the resolution of themore » Navier-Stokes equations as demonstrated by a series of severe test cases including the high-speed viscous flow around a cone, a shock-boundary layer interaction problem, a vacuum apparition problem, the hypersonic flow around a circular cylinder at Mach 100, and the forward-facing step at Mach 3. 36 refs., 7 figs.« less