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PRESSURE CORRECTION METHOD ON unstructured grids

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Journal of Hydrodynamics 2004年第3期16卷 316-324页

作者： LAIXi-jun WANGDe-guan CHENYang NangjingInstituteofGeographyandLimnology ChineseAcademyofSciencesNangjing210008China CollegeofEnvironmentalScienceandEngineering HohaiUniversityNanjing210098China

In this paper, an unstructured, collocated finite volume method for solvingthe Navier-Stokes equations was developed by virtue of auxiliary points. The derivatives weredetermined by the Gauss theorem. The proposed method could provide control volumes with arbitrarygeometry and preserve the second-order accuracy even if highly distorted grids are used. Althougharbitrary number of cell faces can be used, the hybrid quadrilateral/triangular grids are moredesirable for the simplicity of implementation and applications to engineering problems. Thepressure-velocity coupling was treated using a SIMPLE-like algorithm. The Generalized MinimumResidual (GMRES) method with the Incomplete LU (ILU) preconditioner was used to solve linearequations. Four test cases were studied for validating the proposed method. In using this method,grid quality is not important. Thus, engineers can pay mostly attention to physical mechanism ofproblems. Turbulence models can be simply integrated and the method can be straightforwardlyextended to treat three-dimensional problems.

关键词： finite volume method unstructured grids generalized minimum residual(GMRES) method incomplete LU (ILU) preconditioner

High-order compact finite volume methods on unstructured grids with adaptive mesh refinement for solving inviscid and viscous flows

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Chinese Journal of Aeronautics 2018年第9期31卷 1829-1841页

作者： Jianhua PAN Qian WANG Yusi ZHANG Yuxin REN School of Aerospace Engineering Tsinghua University

In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. Mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4 est based on the forest of octrees is adopted. Several two-and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.

关键词： Adaptive mesh refinement Compact stencil High-order finite volume scheme unstructured grids Variational reconstruction

A finite volume method for global electromagnetic induction forward modeling on collocated unstructured grids

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Earth and Planetary Physics 2023年第1期7卷 57-65页

作者： Liang Yin ZhengYong Ren HongBo Yao Cong Yang State Key Laboratory of Lunar and Planetary Sciences Macao University of Science and TechnologyMacaoChina CNSA Macao Center for Space Exploration and Science MacaoChina School of Geosciences and Info-Physics Central South UniversityChangsha 410083China Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring Ministry of Education(Central South University)Changsha 410083China Hunan Key Laboratory of Nonferrous Resources and Geological Hazards Exploration Central South UniversityChangsha 410083China

Global electromagnetic induction provides an efficient way to probe the electrical conductivity in the Earth’s deep *** to the increasing geomagnetic data especially from high-accuracy geomagnetic satellites,inverting the Earth’s three-dimensional conductivity distribution on a global scale becomes attainable.A key requirement in the global conductivity inversion is to have a forward solver with high-accuracy and *** this study,a finite volume method for global electromagnetic induction forward modeling is developed based on unstructured *** polyhedral grids are supported in our algorithms to obtain high geometric *** employ a cell-centered collocated variable arrangement which allows convenient discretization for complex geometries and straightforward implementation of multigrid *** validate the method,we test our code with two synthetic models and compare our finite volume results with an analytical solution and a finite element numerical *** agreements are observed between our solution and other results,indicating acceptable accuracy of the proposed method.

关键词： global electromagnetic induction mantle electrical conductivity finite volume method unstructured grids

A Generalised Lattice Boltzmann Equation on unstructured grids

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Communications in Computational Physics 2008年第2期3卷 342-356页

作者： Stefano Ubertini Sauro Succi Universit`a degli Studi di Roma “Tor Vergata”Dip.Ingegneria MeccanicaVia del Politecnico10133 RomaItalia Istituto Applicazioni del Calcolo CNR Via del Policlinico13700161 RomaItalia.

This paper presents a new finite-volume discretization of a generalised LatticeBoltzmann equation (LBE) on unstructured grids. This equation is the continuumLBE, with the addition of a second order time derivative term (memory), and is derivedfrom a second-order differential form of the semi-discrete Boltzmann equationin its implicit form. The new scheme, named unstructured lattice Boltzmann equationwith memory (ULBEM), can be advanced in time with a larger time-step than the previousunstructured LB formulations, and a theoretical demonstration of the improvedstability is provided. Taylor vortex simulations show that the viscosity is the same aswith standard ULBE and demonstrates that the new scheme improves both stabilityand accuracy. Model validation is also demonstrated by simulating backward-facingstep flow at low and moderate Reynolds numbers, as well as by comparing the reattachmentlength of the recirculating eddy behind the step against experimental andnumerical data available in literature.

关键词： Lattice Boltzmann equation finite-volumes unstructured grids memory term.

A 2D well-balanced, coupled model of water flow, sediment transport,and bed evolution based on unstructured grids with efficient variable storage strategy

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International Journal of Sediment Research 2021年第1期36卷 151-160页

作者： Zhiyuan Yue Qingquan Liu Wei Huang Peng Hu Zhixian Cao Department of Mechanics Beijing Institute of Technology Changjiang Survey Planning Design and Research Co. Ltd (CSPDR) Changjiang River Scientific Research Institute Department of Ocean Engineering Ocean College Zhejiang University State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University

In recent decades,a few Godunov-type,finite volume two-dimensional(2 D) unstructured grid,coupled flow,and sediment models(GF2 DUCM) have been developed for flows over erodible *** kinds of models are generally analyzed as a Vertex Model(VM) that define topography at the cell vertex,which can lead to the non-conservation of mass regarding flow,sediment,and bed ***,a full cellcantered variable storage method(Central Model or CM) is applied as the solution of the GF2 *** this method,terrain elevation is defined at the cell centroids;this accurately describes the physical relations between the water depth and topography *** approach can fully eliminate calculation errors in topography deformation at local cells caused by the interpolation of topography deformation at the cell vertex,and reduced uncertainty in the computation of the GF2 *** model performance is systematically tested using a series of laboratory experiments,which demonstrate the mass conservation feature and high accuracy in reproducing hydrodynamic and morphological processes.

关键词： Two-dimensional coupled model Well-conserved unstructured grids Finite-volume algorithm Erodible bed Central model

A Nominally Second-Order Cell-Centered Finite Volume Scheme for Simulating Three-Dimensional Anisotropic Diffusion Equations on unstructured grids

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Communications in Computational Physics 2014年第9期16卷 841-891页

作者： Pascal Jacq Pierre-Henri Maire Remi Abgrall CEA/CESTA 15 Avenue des Sablieres CS 6000133116 Le Barp cedexFrance. Institut fur Mathematik Universitat ZurichCH-8057 ZurichSwitzerland.

We present a finite volume based cell-centered method for solving diffusion equations on three-dimensional unstructured grids with general tensor *** main motivation concerns the numerical simulation of the coupling between fluid flows and heat *** corresponding numerical scheme is characterized by cell-centered unknowns and a local ***,the scheme results in a global sparse diffusion matrix,which couples only the cell-centered *** space discretization relies on the partition of polyhedral cells into sub-cells and on the partition of cell faces into *** is characterized by the introduction of sub-face normal fluxes and sub-face temperatures,which are auxiliary unknowns.A sub-cellbased variational formulation of the constitutive Fourier law allows to construct an explicit approximation of the sub-face normal heat fluxes in terms of the cell-centered temperature and the adjacent sub-face *** elimination of the sub-face temperatures with respect to the cell-centered temperatures is achieved locally at each node by solving a small and sparse linear *** system is obtained by enforcing the continuity condition of the normal heat flux across each sub-cell interface impinging at the node under *** parallel implementation of the numerical algorithm and its efficiency are described and *** accuracy and the robustness of the proposed finite volume method are assessed by means of various numerical test cases.

关键词： Finite volume methods unstructured grids anisotropic diffusion parallel computing

A Parameter–Free Generalized Moment Limiter for High-Order Methods on unstructured grids

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Advances in Applied Mathematics and Mechanics 2009年第4期1卷 451-480页

作者： Michael Yang Z.J.Wang Department of Aerospace Engineering and CFD Center Iowa State UniversityAmesIA 50011USA

A parameter-free limiting technique is developed for high-order unstructured-grid methods to capture discontinuities when solving hyperbolic conservation *** technique is based on a“troubled-cell”approach,in which cells requiring limiting are first marked,and then a limiter is applied to these marked cells.A parameter-free accuracy-preserving TVD marker based on the cell-averaged solutions and solution derivatives in a local stencil is compared to several other markers in the literature in identifying“troubled cells”.This marker is shown to be reliable and efficient to consistently mark the *** a compact highorder hierarchical moment limiter is developed for arbitrary unstructured *** limiter preserves a degree p polynomial on an arbitrary *** a result,the solution accuracy near smooth local extrema is *** results for the high-order spectral difference methods are provided to illustrate the accuracy,effectiveness,and robustness of the present limiting technique.

关键词： Limiter shock-capturing high-order unstructured grids

Strong Coupled Agglomeration Multigrid for Navier-Stokes Equations on unstructured grids

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Strong Coupled Agglomeration Multigrid for Navier-Stokes Equ...

High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations on unstructured Hexahedral grids

2012年计算机应用与系统建模国际会议

作者： Zongzhe Li Zhenghua Wang Wei Cao Lu Yao School of Computer Science National University of Defence Technology

This paper focused on a series of agglomeration multigrid techniques for the numerical solution of the 2D/3D Reynolds Averaged Navier-Stokes equations on cell-centered unstructured grids, which conform with FVM discretization scheme. We explore a new agglomeration strategy to automated generate coarse grids for multigrid methods, which can conduct to 2D/3D unstructured/hybrid grids. The algorithm based on face weighting, fuse the strongest coupled neigh-bor face to form a new cell in coarsen grid once at a time. The numerical results which conduct on NACA0012 airfoil indicate that nearly optimal computational complexity, this method also shows better complexity than the listed method owing to the better quality of the coarse grid.

关键词： Strong coupled agglomeration unstructured grids Cell-centered Multigrid.

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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.