Volume 24, Issue 5
Application of the GRP Scheme for Cylindrical Compressible Fluid Flows

Rui Chen, Jiequan Li & Baolin Tian

Commun. Comput. Phys., 24 (2018), pp. 1523-1555.

Published online: 2018-06

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  • Abstract

This paper contributes to apply both the direct Eulerian and Lagrangian generalized Riemann problem (GRP) schemes for the simulation of compressible fluid flows in two-dimensional cylindrical geometry. Particular attention is paid to the treatment of numerical boundary conditions at the symmetric center besides the zero velocity (momentum) enforced by the symmetry. The new treatment precisely describes how the thermodynamical variables are discretized near the center using the conservation property. Moreover, the Lagrangian GRP scheme is verified rigorously to satisfy the properties of symmetry and conservation. Numerical results demonstrate the performance of such treatments and the symmetry preserving property of the scheme with second order accuracy both in space and time.

  • Keywords

Euler equations, cylindrical geometry, the generalized Riemann problem (GRP) scheme.

  • AMS Subject Headings

65M08, 76N15, 76L05, 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-1523, author = {}, title = {Application of the GRP Scheme for Cylindrical Compressible Fluid Flows}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {5}, pages = {1523--1555}, abstract = {

This paper contributes to apply both the direct Eulerian and Lagrangian generalized Riemann problem (GRP) schemes for the simulation of compressible fluid flows in two-dimensional cylindrical geometry. Particular attention is paid to the treatment of numerical boundary conditions at the symmetric center besides the zero velocity (momentum) enforced by the symmetry. The new treatment precisely describes how the thermodynamical variables are discretized near the center using the conservation property. Moreover, the Lagrangian GRP scheme is verified rigorously to satisfy the properties of symmetry and conservation. Numerical results demonstrate the performance of such treatments and the symmetry preserving property of the scheme with second order accuracy both in space and time.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0178}, url = {http://global-sci.org/intro/article_detail/cicp/12488.html} }
TY - JOUR T1 - Application of the GRP Scheme for Cylindrical Compressible Fluid Flows JO - Communications in Computational Physics VL - 5 SP - 1523 EP - 1555 PY - 2018 DA - 2018/06 SN - 24 DO - http://dor.org/10.4208/cicp.OA-2017-0178 UR - https://global-sci.org/intro/article_detail/cicp/12488.html KW - Euler equations, cylindrical geometry, the generalized Riemann problem (GRP) scheme. AB -

This paper contributes to apply both the direct Eulerian and Lagrangian generalized Riemann problem (GRP) schemes for the simulation of compressible fluid flows in two-dimensional cylindrical geometry. Particular attention is paid to the treatment of numerical boundary conditions at the symmetric center besides the zero velocity (momentum) enforced by the symmetry. The new treatment precisely describes how the thermodynamical variables are discretized near the center using the conservation property. Moreover, the Lagrangian GRP scheme is verified rigorously to satisfy the properties of symmetry and conservation. Numerical results demonstrate the performance of such treatments and the symmetry preserving property of the scheme with second order accuracy both in space and time.

Rui Chen, Jiequan Li & Baolin Tian. (2020). Application of the GRP Scheme for Cylindrical Compressible Fluid Flows. Communications in Computational Physics. 24 (5). 1523-1555. doi:10.4208/cicp.OA-2017-0178
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