TY - JOUR

T1 - Towards positivity preservation for monolithic two-way solid-fluid coupling

AU - Patkar, Saket

AU - Aanjaneya, Mridul

AU - Lu, Wenlong

AU - Lentine, Michael

AU - Fedkiw, Ronald

N1 - Funding Information:
Research supported in part by ONR N00014-13-1-0346 , ONR N00014-11-1-0707 , ONR N-00014-11-1-0027, ONR N00014-09-1-0101 , ARL AHPCRC W911NF-07-0027 , and the Intel Science and Technology Center for Visual Computing . S.P. was supported in part by the Stanford Graduate Fellowship. M.A. was supported in part by the Nokia Research Center. Computing resources were provided in part by ONR N00014-05-1-0479 . We would like to thank Prof. Xiangxiong Zhang and Aamer Haque for providing us with the analytic solutions to the Sedov blast wave problem.
Publisher Copyright:
© 2016 Elsevier Inc.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - We consider complex scenarios involving two-way coupled interactions between compressible fluids and solid bodies under extreme conditions where monolithic, as opposed to partitioned, schemes are preferred for maintaining stability. When considering such problems, spurious numerical cavitation can be quite common and have deleterious consequences on the flow field stability, accuracy, etc. Thus, it is desirable to devise numerical methods that maintain the positivity of important physical quantities such as density, internal energy and pressure. We begin by showing that for an arbitrary flux function, one can put conditions on the time step in order to preserve positivity by solving a linear equation for density fluxes and a quadratic equation for energy fluxes. Our formulation is independent of the underlying equation of state. After deriving the method for forward Euler time integration, we further extend it to higher order accurate Runge-Kutta methods. Although the scheme works well in general, there are some cases where no lower bound on the size of the allowable time step exists. Thus, to prevent the size of the time step from becoming arbitrarily small, we introduce a conservative flux clamping scheme which is also positivity preserving. Exploiting the generality of our formulation, we then design a positivity preserving scheme for a semi-implicit approach to time integration that solves a symmetric positive definite linear system to determine the pressure associated with an equation of state. Finally, this modified semi-implicit approach is extended to monolithic two-way solid-fluid coupling problems for modeling fluid structure interactions such as those generated by blast waves impacting complex solid objects.

AB - We consider complex scenarios involving two-way coupled interactions between compressible fluids and solid bodies under extreme conditions where monolithic, as opposed to partitioned, schemes are preferred for maintaining stability. When considering such problems, spurious numerical cavitation can be quite common and have deleterious consequences on the flow field stability, accuracy, etc. Thus, it is desirable to devise numerical methods that maintain the positivity of important physical quantities such as density, internal energy and pressure. We begin by showing that for an arbitrary flux function, one can put conditions on the time step in order to preserve positivity by solving a linear equation for density fluxes and a quadratic equation for energy fluxes. Our formulation is independent of the underlying equation of state. After deriving the method for forward Euler time integration, we further extend it to higher order accurate Runge-Kutta methods. Although the scheme works well in general, there are some cases where no lower bound on the size of the allowable time step exists. Thus, to prevent the size of the time step from becoming arbitrarily small, we introduce a conservative flux clamping scheme which is also positivity preserving. Exploiting the generality of our formulation, we then design a positivity preserving scheme for a semi-implicit approach to time integration that solves a symmetric positive definite linear system to determine the pressure associated with an equation of state. Finally, this modified semi-implicit approach is extended to monolithic two-way solid-fluid coupling problems for modeling fluid structure interactions such as those generated by blast waves impacting complex solid objects.

KW - Compressible flow

KW - Fluid simulation

KW - Monolithic solid-fluid coupling

KW - Positivity preservation

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U2 - 10.1016/j.jcp.2016.02.010

DO - 10.1016/j.jcp.2016.02.010

M3 - Article

AN - SCOPUS:84958267944

SN - 0021-9991

VL - 312

SP - 82

EP - 114

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -