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A Conservative Lagrangian Scheme for Solving Compressible Fluid Flows with Multiple Internal Energy Equations

Communications in Computational Physics 2012年第10期12卷 1307-1328页

作者： Juan Cheng Chi-Wang Shu Qinghong Zeng National Key Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Institute of Applied Physics and Computational Mathematics Beijing 100088China

Lagrangianmethods arewidely used inmany fields formulti-material compressible flow simulations such as in astrophysics and inertial confinement fusion(ICF),due to their distinguished advantage in capturing material interfaces automatically.In some of these applications,multiple internal energy equations such as those for electron,ion and radiation are involved.In the past decades,several staggeredgrid based Lagrangian schemes have been developed which are designed to solve the internal energy equation directly.These schemes can be easily extended to solve problems with multiple internal energy equations.However such schemes are typically not conservative for the total energy.Recently,significant progress has been made in developing cell-centered Lagrangian schemes which have several good properties such as conservation for all the conserved variables and easiness for remapping.However,these schemes are commonly designed to solve the Euler equations in the form of the total energy,therefore they cannot be directly applied to the solution of either the single internal energy equation or the multiple internal energy equations without significant modifications.Such modifications,if not designed carefully,may lead to the loss of some of the nice properties of the original schemes such as conservation of the total energy.In this paper,we establish an equivalency relationship between the cell-centered discretizations of the Euler equations in the forms of the total energy and of the internal energy.By a carefully designed modification in the implementation,the cell-centered Lagrangian scheme can be used to solve the compressible fluid flow with one or multiple internal energy equations and meanwhile it does not lose its total energy conservation property.An advantage of this approach is that it can be easily applied to many existing large application codes which are based on the framework of solving multiple internal energy equations.Several two dimensional numerical examples for both Euler equations and three-temperatu

关键词： Lagrangian scheme conservative cell-centered internal energy equation compressible fluid flow three-temperaturemodel

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Improvement on Spherical Symmetry in Two-Dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes

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Communications in Computational Physics 2012年第4期11卷 1144-1168页

作者： Juan Cheng Chi-Wang Shu Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

In[14],Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations of compressible gas dynamics in cylindrical coordinates.These schemes use a node-based discretization of the numerical fluxes.The control volume version has several distinguished properties,including the conservation of mass,momentum and total energy and compatibility with the geometric conservation law(GCL).However it also has a limitation in that it cannot preserve spherical symmetry for one-dimensional spherical flow.An alternative is also given to use the first order area-weighted approach which can ensure spherical symmetry,at the price of sacrificing conservation of momentum.In this paper,we apply the methodology proposed in our recent work[8]to the first order control volume scheme of Maire in[14]to obtain the spherical symmetry property.The modified scheme can preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid,andmeanwhile itmaintains its original good properties such as conservation and GCL.Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of symmetry,non-oscillation and robustness properties.

关键词： Control volume Lagrangian scheme spherical symmetry preservation conservative cell-centered compressible flow cylindrical coordinates

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The Confinement Effect of Inert Materials on the Detonation of Insensitive High Explosives

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World Journal of Mechanics 2018年第5期8卷 161-181页

作者： Ming Yu Institute of Applied Physics and Computational Mathematics Beijing China

The paper aims to theoretically and numerically investigate the confinement effect of inert materials on the detonation of insensitive high explosives. An improved shock polar theory based on the Zeldovich-von Neumann-Döring model of explosive detonation is established and can fully categorize the confinement interactions between insensitive high explosive and inert materials into six types for the inert materials with smaller sonic velocities than the Chapman-Jouguet velocity of explosive detonation. To confirm the theoretical categorization and obtain the flow details, a second-order, cell-centered Lagrangian hydrodynamic method based on the characteristic theory of the two-dimensional first-order hyperbolic partial differential equations with Ignition-Growth chemistry reaction law is proposed and can exactly numerically simulate the confinement interactions. The numerical result confirms the theoretical categorization and can further merge six types of interaction styles into five types for the inert materials with smaller sonic velocity, moreover, the numerical method can give a new type of interaction style existing a precursor wave in the confining inert material with a larger sonic velocity than the Chapman-Jouguet velocity of explosive detonation, in which a shock polar theory is invalid. The numerical method can also give the effect of inert materials on the edge angles of detonation wave front.

关键词： Detonation Confinement Effect Insensitive High Explosives Shock Polar Theory cell-centered Lagrangian Method

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Strong Coupled Agglomeration Multigrid for Navier-Stokes Equations on Unstructured Grids

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

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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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