TY - JOUR

T1 - A rezoning-free CESE Scheme for solving the Compressible Euler Equations on Moving Unstructured Meshes

AU - Shen, Hua

AU - Parsani, Matteo

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). We would like to acknowledge the computer time provided by the KAUST Extreme Computing Research Center (ECRC).

PY - 2019/8/2

Y1 - 2019/8/2

N2 - We construct a space-time conservation element and solution element (CESE) scheme for solving the compressible Euler equations on moving meshes (CESE-MM) which allow an arbitrary motion for each of the mesh points. The scheme is a direct extension of a purely Eulerian CESE scheme that was previously implemented on hybrid unstructured meshes (Shen et al., J. Comput. Phys., 2015). It adopts a staggered mesh in space and time such that the physical variables are continuous across the interfaces of the adjacent space-time control volumes and, therefore, a Riemann solver is not required to calculate interface fluxes or the node velocities. Moreover, the staggered mesh can significantly alleviate mesh tangles so that the time step can be kept at an acceptable level without using any rezoning operation. The discretization of the integral space-time conservation law is completely based on the physical space-time control volume, thereby satisfying the physical and geometrical conservation laws. Plenty of numerical examples are carried out to validate the accuracy and robustness of the CESE-MM scheme.

AB - We construct a space-time conservation element and solution element (CESE) scheme for solving the compressible Euler equations on moving meshes (CESE-MM) which allow an arbitrary motion for each of the mesh points. The scheme is a direct extension of a purely Eulerian CESE scheme that was previously implemented on hybrid unstructured meshes (Shen et al., J. Comput. Phys., 2015). It adopts a staggered mesh in space and time such that the physical variables are continuous across the interfaces of the adjacent space-time control volumes and, therefore, a Riemann solver is not required to calculate interface fluxes or the node velocities. Moreover, the staggered mesh can significantly alleviate mesh tangles so that the time step can be kept at an acceptable level without using any rezoning operation. The discretization of the integral space-time conservation law is completely based on the physical space-time control volume, thereby satisfying the physical and geometrical conservation laws. Plenty of numerical examples are carried out to validate the accuracy and robustness of the CESE-MM scheme.

UR - http://hdl.handle.net/10754/656401

UR - https://linkinghub.elsevier.com/retrieve/pii/S002199911930542X

UR - http://www.scopus.com/inward/record.url?scp=85070186472&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.108858

DO - 10.1016/j.jcp.2019.108858

M3 - Article

VL - 397

SP - 108858

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -