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High-Order Multidomain spectral difference Method for the Navier-Stokes Equations on Unstructured Hexahedral Grids

Communications in Computational Physics 2007年第2期2卷 310-333页

作者： Yuzhi Sun Z.J.Wang Yen Liu Department of Aerospace Engineering Iowa State University2271 Howe HallAmesIA 50011USA NASA Ames Research Center Mail Stop T27B-1Moffett FieldCA 94035USA

A high order multidomain spectral difference method has been developed for the three dimensional Navier-Stokes equations on unstructured hexahedral *** method is easy to implement since it involves one-dimensional operations only,and does not involve surface or volume *** reconstructions are obtained by distributing solution and flux points in a geometrically similar manner in a unit *** concepts of the Riemann solver and high-order local representations are applied to achieve conservation and high order *** this paper,accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical *** order of accuracy and spectral convergence are obtained for the propagation of an isotropic vortex and Couette *** capability of the method for both inviscid and viscous flow problems with curved boundaries is also demonstrated.

关键词： High order unstructured grids spectral difference Navier-Stokes.

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Large Eddy Simulation of Flow over a Cylinder Using High-Order spectral difference Method

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Advances in Applied Mathematics and Mechanics 2010年第4期2卷 451-466页

作者： Abrar H.Mohammad Z.J.Wang Chunlei Liang Department of Aerospace Engineering Iowa State UniversityAmesIA 50011U.S.A Department of Aeronautics and Astronautics Stanford UniversityStanfordCA 94305U.S.A

Large eddy simulation of the flow over a circular cylinder at Reynolds number ReD=2580 has been studied with a high-order unstructured spectral difference *** and polynomial refinement studies were carried out to assess numerical *** mean and fluctuating velocity fields in the wake of a circular cylinder were compared with PIV experimental *** numerical results are in excellent agreement with the experimental data for both the mean velocity and Reynolds stresses using the high-order SD *** wake characteristics such as the recirculation bubble length,vortex formation length and maximum intensity of the velocity fluctuations have also been predicted *** numerical simulations demonstrated the potential of the high-order SD method in accurate large eddy simulation of physically complex problems.

关键词： LES spectral difference circular cylinder coherent structures vortex shedding

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Efficient Implicit Non-linear LU-SGS Approach for Compressible Flow Computation Using High-Order spectral difference Method

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Communications in Computational Physics 2009年第2期5卷 760-778页

作者： Yuzhi Sun Z.J.Wang Yen Liu Department of Aerospace Engineering Iowa State UniversityAmesIA 50011USA NASA Ames Research Center Moffett FieldCA 94035USA

An implicit non-linear lower-upper symmetric Gauss-Seidel(LU-SGS)solution algorithm has been developed for a high-order spectral difference Navier-Stokes solver on unstructured hexahedral *** non-linear LU-SGS solver is preconditioned by a block element matrix,and the system of equations is then solved with the LU decomposition *** large sparse Jacobian matrix is computed numerically,resulting in extremely simple operations for arbitrarily complex residual *** inviscid and viscous test cases were performed to evaluate the *** implicit solver has shown speedup of 1 to 2 orders of magnitude over the multi-stage Runge-Kutta time integration scheme.

关键词： High order unstructured grids spectral difference Navier-Stokes implicit

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An Exact Propagator for Solving the Triatomic Reactive Schrodinger Equation

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Chinese Journal of Chemical Physics 2017年第6期30卷 761-770,I0003页

作者：李学明孙志刚中国科学院大连化学物理研究所分子反应动力学国家重点实验室和理论与计算化学中心大连116023 中国科学院大学北京100049

The exact short time propagator, in a form similar to the Crank-Nicholson method but in the spirit of spectrally transformed Hamiltonian, was proposed to solve the triatomic reactive time-dependent schrodinger equation. This new propagator is exact and unconditionally convergent for calculating reactive scattering processes with large time step sizes. In order to improve the computational efficiency, the spectral difference method was applied. This resulted the Hamiltonian with elements confined in a narrow diagonal band. In contrast to our previous theoretical work, the discrete variable representation was applied and resulted in full Hamiltonian matrix. As examples, the collision energy-dependent probability of the triatomic H＋H2 and O＋O2 reaction are calculated. The numerical results demonstrate that this new propagator is numerically accurate and capable of propagating the wave packet with large time steps. However, the efficiency and accuracy of this new propagator strongly depend on the mathematical method for solving the involved linear equations and the choice of preconditioner.

关键词： Time-dependent wavepacket method spectral difference spectrally transformed Hamiltonian Exact short time propagator Reactive scattering

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