A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes

Zhang, Zeng-Chan; Yu, S. T. John; Chang, Sin-Chung

doi:10.1006/jcph.2001.6934

Cited by 160 publications

(68 citation statements)

References 22 publications

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“…The spacetime conservation element / solution element (CE/SE) method is a HRSC method introduced by Chang (1995) for 1D flows (see Zhang et al, 2002 and references therein for 2D and 3D extensions using structured and unstructured meshes). In contrast with conventional FV methods based on the Reynolds transport theorem, in which space and time are treated separately, the CE/SE method adopts an integral form of spacetime flux conservation as the cornerstone for the subsequent discretization.…”

Section: Ce/se Methodsmentioning

confidence: 99%

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

Martí

Müller

2015

Living Rev Comput Astrophys

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An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates. Article RevisionsLiving Reviews supports two ways of keeping its articles up-to-date:Fast-track revision. A fast-track revision provides the author with the opportunity to add short notices of current research results, trends and developments, or important publications to the article. A fast-track revision is refereed by the responsible subject editor. If an article has undergone a fast-track revision, a summary of changes will be listed here.Major update. A major update will include substantial changes and additions and is subject to full external refereeing. It is published with a new publication number.For detailed documentation of an article's evolution, please refer to the history document of the article's online version at http://dx

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Section: Ce/se Methodsmentioning

confidence: 99%

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

Martí

Müller

2015

Living Rev Comput Astrophys

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“…However researchers have found defects in the original CE/SE schemes, such as the complication of mesh structure, the absence of high-order accuracy schemes and the difficulty to extend to three-dimensional situation. To solve these problems, Zhang et al [10], Zhang et al [11] and Liu et al [5,6] have made some progress in this area.…”

Section: Improved Ce/se Methodsmentioning

confidence: 99%

New numerical algorithms in SUPER CE/SE and their applications in explosion mechanics

Wang

Liu

2010

Sci. China Phys. Mech. Astron.

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The new numerical algorithms in SUPER/CESE and their applications in explosion mechanics are studied. The researched algorithms and models include an improved CE/SE (space-time Conservation Element and Solution Element) method, a local hybrid particle level set method, three chemical reaction models and a two-fluid model. Problems of shock wave reflection over wedges, explosive welding, cellular structure of gaseous detonations and two-phase detonations in the gas-droplet system are simulated by using the above-mentioned algorithms and models. The numerical results reveal that the adopted algorithms have many advantages such as high numerical accuracy, wide application field and good compatibility. The numerical algorithms presented in this paper may be applied to the numerical research of explosion mechanics. new algorithm, SUPER CE/SE, numerical simulation, explosion mechanicsThe research of explosion mechanics, usually involving many disciplines such as compressible flows, incompressible flows, elastic-plastic flows, chemically reacting flows and two-phase flows, contributes significantly to the field of industry, aeronautics, and military engineering. Numerical simulation of explosion mechanics needs not only accurate numerical schemes and interface capturing methods, but also a perfect combination of the selected numerical algorithms and the physical and chemical models.The imported commercial software, such as LS-DYNA and AUTODYN, currently plays a dominant role in the application of explosion mechanics in China. Further development based on the imported commercial software is quite difficult, because the kernel modules of the software are always held as commercial secrets. The software of computational explosion mechanics in China has undergone a step-by-step development. The well-established software packages include METH This paper has studied the new numerical algorithms in SUPER CE/SE and their applications in explosion mechanics. SUPER CE/SE uses an improved CE/SE (space-time Conservation Element and Solution Element) method [5,6] to discrete governing equations, a local hybrid particle level set method to capture the interface, and a two-fluid model to treat two-phase flows. SUPER CE/SE is also able to adopt common chemical reaction models, such as two-step, detailed and Sichel's two-step chemical reaction models. With the above algorithms and models, problems of shock wave reflection over wedges, explosive welding, cellular structure of gaseous detonations and two-phase detonations in gas-droplet system are investigated. Comparisons and dis-

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“…By using Gauss' divergence theorem in 3 E , we have will be based on the modified CESE method for a quadrilateral mesh [19]. To be concise, our discussion of the CESE method will be focused on a uniform quadrilateral mesh.…”

Section: The Cese Methodsmentioning

confidence: 99%

“…In the present paper, we report the application of the Space-Time Conservation Element and Solution Element (CESE) method [17][18][19][20] to solve the two-dimensional MHD equations. Four approaches are employed: (i) the original CESE method without any additional treatment for ∇⋅B = 0, (ii) a simple modification procedure to update the spatial derivatives of B after each time marching step such that ∇⋅B = 0 is enforced at all mesh nodes, (iii) an extended CESE method based on the constraint-transport procedure, and (iv) the projection method coupled with the CESE method.…”

Section: Introductionmentioning

confidence: 99%

Solving the MHD equations by the space–time conservation element and solution element method

Zhang

Lin

et al. 2006

Journal of Computational Physics

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We apply the Space-Time Conservation Element and Solution Element (CESE) method to solve the ideal MHD equations with special emphasis on satisfying the divergence free constraint of magnetic field, i.e., ∇⋅B = 0. In the setting of the CESE method, four approaches are employed: (i) the original CESE method without any additional treatment,(ii) a simple corrector procedure to update the spatial derivatives of magnetic field B after each time marching step to enforce ∇⋅B = 0 at all mesh nodes, (iii) an constraint-transport method by using a special staggered mesh to calculate magnetic field B, and (iv) the projection method by solving a Poisson solver after each time marching step. To demonstrate the capabilities of these methods, two benchmark MHD flows are calculated (i) a rotated one-dimensional MHD shock tube problem, and (ii) a MHD vortex problem.The results show no differences between different approaches and all results compare favorably with previously reported data.3

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A Space-Time Conservation Element and Solution Element Method for Solving the Two- and Three-Dimensional Unsteady Euler Equations Using Quadrilateral and Hexahedral Meshes

Cited by 160 publications

References 22 publications

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

New numerical algorithms in SUPER CE/SE and their applications in explosion mechanics

Solving the MHD equations by the space–time conservation element and solution element method

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