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Volume 36, Issue 2
Asymptotic-Preserving Schemes for Kinetic-Fluid Modeling of Mixture Flows

Yiwen Lin & Shi Jin

DOI: 10.4208/cicp.OA-2023-0298

Commun. Comput. Phys., 36 (2024), pp. 319-347.

Published online: 2024-09

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  • Abstract

We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck equations. We design an asymptotic-preserving numerical scheme to approximate the system. The scheme is based on suitable implicit treatment of the stiff drag force term as well as the Fokker-Planck operator, and can be formally shown to capture the hydrodynamic limit with time step and mesh size independent of the Stokes number. Numerical examples illustrate the accuracy and asymptotic behavior of the scheme, with several interesting applications.

  • Keywords

Particulate flows, coupled kinetic-fluid model, Vlasov-Fokker-Planck-Navier-Stokes equations, asymptotic preserving schemes.

  • AMS Subject Headings

35Q35, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-36-319, author = {Lin , Yiwen and Jin , Shi}, title = {Asymptotic-Preserving Schemes for Kinetic-Fluid Modeling of Mixture Flows}, journal = {Communications in Computational Physics}, year = {2024}, volume = {36}, number = {2}, pages = {319--347}, abstract = {

We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck equations. We design an asymptotic-preserving numerical scheme to approximate the system. The scheme is based on suitable implicit treatment of the stiff drag force term as well as the Fokker-Planck operator, and can be formally shown to capture the hydrodynamic limit with time step and mesh size independent of the Stokes number. Numerical examples illustrate the accuracy and asymptotic behavior of the scheme, with several interesting applications.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0298}, url = {http://global-sci.org/intro/article_detail/cicp/23385.html} }
TY - JOUR T1 - Asymptotic-Preserving Schemes for Kinetic-Fluid Modeling of Mixture Flows AU - Lin , Yiwen AU - Jin , Shi JO - Communications in Computational Physics VL - 2 SP - 319 EP - 347 PY - 2024 DA - 2024/09 SN - 36 DO - http://doi.org/10.4208/cicp.OA-2023-0298 UR - https://global-sci.org/intro/article_detail/cicp/23385.html KW - Particulate flows, coupled kinetic-fluid model, Vlasov-Fokker-Planck-Navier-Stokes equations, asymptotic preserving schemes. AB -

We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck equations. We design an asymptotic-preserving numerical scheme to approximate the system. The scheme is based on suitable implicit treatment of the stiff drag force term as well as the Fokker-Planck operator, and can be formally shown to capture the hydrodynamic limit with time step and mesh size independent of the Stokes number. Numerical examples illustrate the accuracy and asymptotic behavior of the scheme, with several interesting applications.

Yiwen Lin & Shi Jin. (2024). Asymptotic-Preserving Schemes for Kinetic-Fluid Modeling of Mixture Flows. Communications in Computational Physics. 36 (2). 319-347. doi:10.4208/cicp.OA-2023-0298
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