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Improving the High Order spectral volume Formulation Using a Diffusion Regulator

Communications in Computational Physics 2012年第6期12卷 247-260页

作者： Ravi Kannan Zhijian Wang CFD Research Corporation 215Wynn DriveHuntsvilleAL 35805USA Iowa State University Howe HallAmesIA 50011USA

The concept of diffusion regulation(DR)was originally proposed by Jaisankar for traditional second order finite volume Euler *** was used to decrease the inherent dissipation associated with using approximate Riemann *** this paper,the above concept is extended to the high order spectral volume(SV)*** DR formulation was used in conjunction with the Rusanov flux to handle the inviscid flux *** experiments were conducted to compare and contrast the original and the DR *** experiments demonstrated(i)retention of high order accuracy for the new formulation,(ii)higher fidelity of the DR formulation,when compared to the original scheme for all orders and(iii)straightforward extension to Navier Stokes equations,since the DR does not interfere with the discretization of the viscous *** general,the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.

关键词： Diffusion regulation spectral volume high-order Rusanov flux Navier Stokes equations

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A High Order spectral volume Formulation for Solving Equations Containing Higher Spatial Derivative Terms II:Improving the Third Derivative Spatial Discretization Using the LDG2 Method

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Communications in Computational Physics 2012年第8期12卷 767-788页

作者： Ravi Kannan CFD Research Corporation 215Wynn DriveHuntsville AL 35805USA

In this paper,the second in a series,we improve the discretization of the higher spatial derivative terms in a spectral volume(SV)*** motivation for the above comes from[***.,46(2),314–328],wherein the authors developed a variant of the LDG(Local Discontinuous Galerkin)flux discretization *** variant(aptly named LDG2),not only displayed higher accuracy than the LDG approach,but also vastly reduced its unsymmetrical *** this paper,we adapt the LDG2 formulation for discretizing third derivative terms.A linear Fourier analysis was performed to compare the dispersion and the dissipation properties of the LDG2 and the LDG *** results of the analysis showed that the LDG2 scheme(i)is stable for 2nd and 3rd orders and(ii)generates smaller dissipation and dispersion errors than the LDG formulation for all the *** 4th order LDG2 scheme is howevermildly unstable:as the real component of the principal eigen value briefly becomes *** order to circumvent the above,a weighted average of the LDG and the LDG2 fluxes was used as the final numerical *** a weight of 1.5%for the LDG(i.e.,98.5%for the LDG2)was sufficient tomake the scheme *** scheme is still predominantly LDG2 and hence generated smaller dissipation and dispersion errors than the LDG *** experiments are performed to validate the *** general,the numerical results are very promising and indicate that the approach has a great potential for higher dimension Korteweg-de Vries(KdV)type problems.

关键词： spectral volume LDG2 LDG higher spatial derivative terms KDV Fourier analysis

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A High Order spectral volume Formulation for Solving Equations Containing Higher Spatial Derivative Terms:Formulation and Analysis for Third Derivative Spatial Terms Using the LDG Discretization Procedure

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Communications in Computational Physics 2011年第10期10卷 1257-1279页

作者： Ravi Kannan CFD Research Corporation 215Wynn DriveHuntsvilleAL 35805USA

In this paper,we develop a formulation for solving equations containing higher spatial derivative terms in a spectral volume(SV)context;more specifically the emphasis is on handling equations containing third derivative *** formulation is based on the LDG(Local Discontinuous Galerkin)flux discretization method,originally employed for viscous equations containing second derivatives.A linear Fourier analysis was performed to study the dispersion and the dissipation properties of the new *** Fourier analysis was utilized for two purposes:firstly to eliminate all the unstable SV partitions,secondly to obtain the optimal SV *** experiments are performed to illustrate the capability of this *** this formulation is extremely local,it can be easily parallelized and a h-p adaptation is relatively straightforward to *** general,the numerical results are very promising and indicate that the approach has a great potential for higher dimension Korteweg-de Vries(KdV)type problems.

关键词： spectral volume LDG higher spatial derivative terms KDV Fourier analysis

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An Implicit LU-SGS Scheme for the spectral volume Method on Unstructured Tetrahedral Grids

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Communications in Computational Physics 2009年第10期6卷 978-996页

作者： Takanori Haga Keisuke Sawada Z.J.Wang Department of Aerospace Engineering Tohoku UniversitySendai 980-8579Japan Department of Aerospace Engineering Iowa State UniversityAmesIA 50011USA

An efficient implicit lower-upper symmetric Gauss-Seidel(LU-SGS)solution approach has been applied to a high order spectral volume(SV)method for unstructured tetrahedral *** LU-SGS solver is preconditioned by the block element matrix,and the system of equations is then solved with a LU *** compact feature of SV reconstruction facilitates the efficient solution algorithm even for high order *** developed implicit solver has shown more than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme for typical inviscid and viscous problems.A convergence to a high order solution for high Reynolds number transonic flow over a 3D wing with a one equation turbulence model is also indicated.

关键词： High-order unstructured grid spectral volume implicit method

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