Volume 24, Issue 3
A High-Resolution Cell-Centered Lagrangian Method with a Vorticity-Based Adaptive Nodal Solver for Two-Dimensional Compressible Euler Equations

Jin Qi, Baolin Tian & Jiequan Li

Commun. Comput. Phys., 24 (2018), pp. 774-790.

Published online: 2018-05

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  • Abstract

In this work, a second-order high-resolution LAgrangian method with a Vorticity-based Adaptive Nodal Solver (LAVANS) is proposed to overcome the numerical difficulty of traditional Lagrangian methods for the simulation of multidimensional flows. The work mainly include three aspects to improve the performance of the traditional CAVEAT-type cell-centered Lagrangian method. First, a vorticity-based adaptive least-squares method for vertex velocity computation is proposed to suppress nonphysical mesh distortion caused by the traditional five-point-stencil least-squares method. Second, a simple interface flux modification is proposed such that the geometry conservation law is satisfied. Third, a generalized Riemann problem solver is employed in the LAVANS scheme to achieve one-step time-space second-order accuracy. Some typical benchmark numerical tests validate the performance of the LAVANS scheme.

  • Keywords

Cell-centered Lagrangian scheme, CAVEAT scheme, geometry conservation law, vertex velocity, generalized Riemann problem (GRP) solver.

  • AMS Subject Headings

76M12, 76N15, 76T99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-774, author = {}, title = {A High-Resolution Cell-Centered Lagrangian Method with a Vorticity-Based Adaptive Nodal Solver for Two-Dimensional Compressible Euler Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {3}, pages = {774--790}, abstract = {

In this work, a second-order high-resolution LAgrangian method with a Vorticity-based Adaptive Nodal Solver (LAVANS) is proposed to overcome the numerical difficulty of traditional Lagrangian methods for the simulation of multidimensional flows. The work mainly include three aspects to improve the performance of the traditional CAVEAT-type cell-centered Lagrangian method. First, a vorticity-based adaptive least-squares method for vertex velocity computation is proposed to suppress nonphysical mesh distortion caused by the traditional five-point-stencil least-squares method. Second, a simple interface flux modification is proposed such that the geometry conservation law is satisfied. Third, a generalized Riemann problem solver is employed in the LAVANS scheme to achieve one-step time-space second-order accuracy. Some typical benchmark numerical tests validate the performance of the LAVANS scheme.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0068}, url = {http://global-sci.org/intro/article_detail/cicp/12280.html} }
TY - JOUR T1 - A High-Resolution Cell-Centered Lagrangian Method with a Vorticity-Based Adaptive Nodal Solver for Two-Dimensional Compressible Euler Equations JO - Communications in Computational Physics VL - 3 SP - 774 EP - 790 PY - 2018 DA - 2018/05 SN - 24 DO - http://dor.org/10.4208/cicp.OA-2017-0068 UR - https://global-sci.org/intro/article_detail/cicp/12280.html KW - Cell-centered Lagrangian scheme, CAVEAT scheme, geometry conservation law, vertex velocity, generalized Riemann problem (GRP) solver. AB -

In this work, a second-order high-resolution LAgrangian method with a Vorticity-based Adaptive Nodal Solver (LAVANS) is proposed to overcome the numerical difficulty of traditional Lagrangian methods for the simulation of multidimensional flows. The work mainly include three aspects to improve the performance of the traditional CAVEAT-type cell-centered Lagrangian method. First, a vorticity-based adaptive least-squares method for vertex velocity computation is proposed to suppress nonphysical mesh distortion caused by the traditional five-point-stencil least-squares method. Second, a simple interface flux modification is proposed such that the geometry conservation law is satisfied. Third, a generalized Riemann problem solver is employed in the LAVANS scheme to achieve one-step time-space second-order accuracy. Some typical benchmark numerical tests validate the performance of the LAVANS scheme.

Jin Qi, Baolin Tian & Jiequan Li. (2020). A High-Resolution Cell-Centered Lagrangian Method with a Vorticity-Based Adaptive Nodal Solver for Two-Dimensional Compressible Euler Equations. Communications in Computational Physics. 24 (3). 774-790. doi:10.4208/cicp.OA-2017-0068
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