FIVER

FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps. A robust finite volume method for the solution of high-speed compressible flows in multi-material domains involving arbitrary equations of state and large density jumps is presented. The global domain of interest can include a moving or deformable subdomain that furthermore may undergo topological changes due to, for example, crack propagation. The key components of the proposed method include: (a) the definition of a discrete surrogate material interface, (b) the computation of a reliable approximation of the fluid state vector on each side of a discrete material interface via the construction and solution of a local, exact, two-phase Riemann problem, (c) the algebraic solution of this auxiliary problem when the equation of state allows it, and (d) the solution of this two-phase Riemann problem using sparse grid tabulations otherwise. The proposed computational method is illustrated with the three-dimensional simulation of the dynamics of an underwater explosion bubble.


References in zbMATH (referenced in 18 articles )

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  1. Bempedelis, Nikolaos; Ventikos, Yiannis: A simplified approach for simulations of multidimensional compressible multicomponent flows: the grid-aligned ghost fluid method (2020)
  2. Zeng, Xianyi; Li, Kangan; Scovazzi, Guglielmo: An ALE/embedded boundary method for two-material flow simulations (2019)
  3. Chen, Li; Li, Ruo; Yao, Chengbao: An approximate solver for multi-medium Riemann problem with Mie-Grüneisen equations of state (2018)
  4. Chung, Howard; Cao, Shunxiang; Philen, Michael; Beran, Philip S.; Wang, Kevin G.: CFD-CSD coupled analysis of underwater propulsion using a biomimetic fin-and-joint system (2018)
  5. Huang, Daniel Z.; De Santis, Dante; Farhat, Charbel: A family of position- and orientation-independent embedded boundary methods for viscous flow and fluid-structure interaction problems (2018)
  6. Abgrall, Rémi; Tokareva, Svetlana: Staggered grid residual distribution scheme for Lagrangian hydrodynamics (2017)
  7. Main, Alex; Zeng, Xianyi; Avery, Philip; Farhat, Charbel: An enhanced FIVER method for multi-material flow problems with second-order convergence rate (2017)
  8. Banks, J. W.; Henshaw, W. D.; Kapila, A. K.; Schwendeman, D. W.: An added-mass partition algorithm for fluid-structure interactions of compressible fluids and nonlinear solids (2016)
  9. Hachem, E.; Khalloufi, M.; Bruchon, J.; Valette, R.; Mesri, Y.: Unified adaptive variational multiscale method for two phase compressible-incompressible flows (2016)
  10. Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri: Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. I: The one-dimensional case (2016)
  11. Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri: Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. II: The two-dimensional case (2016)
  12. Zhu, Ling; Zhang, Zhiyue; Li, Zhilin: An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions (2015)
  13. Balajewicz, Maciej; Farhat, Charbel: Reduction of nonlinear embedded boundary models for problems with evolving interfaces (2014)
  14. Cheng, Juan; Shu, Chi-Wang: Positivity-preserving Lagrangian scheme for multi-material compressible flow (2014)
  15. Farhat, Charbel; Lakshminarayan, Vinod K.: An ALE formulation of embedded boundary methods for tracking boundary layers in turbulent fluid-structure interaction problems (2014)
  16. Jemison, Matthew; Sussman, Mark; Arienti, Marco: Compressible, multiphase semi-implicit method with moment of fluid interface representation (2014)
  17. Main, Alex; Farhat, Charbel: A second-order time-accurate implicit finite volume method with exact two-phase Riemann problems for compressible multi-phase fluid and fluid-structure problems (2014)
  18. Farhat, Charbel; Gerbeau, Jean-Frédéric; Rallu, Arthur: FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps (2012)