Efficient symmetric positive definite second-order accurate monolithic solver for fluid/solid interactions

Frédéric Gibou; Chohong Min

doi:10.1016/j.jcp.2012.01.009

Efficient symmetric positive definite second-order accurate monolithic solver for fluid/solid interactions

Frédéric Gibou, Chohong Min

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

Abstract

We introduce a robust and efficient method to simulate strongly coupled (monolithic) fluid/rigid-body interactions. We take a fractional step approach, where the intermediate state variables of the fluid and of the solid are solved independently, before their interactions are enforced via a projection step. The projection step produces a symmetric positive definite linear system that can be efficiently solved using the preconditioned conjugate gradient method. In particular, we show how one can use the standard preconditioner used in standard fluid simulations to precondition the linear system associated with the projection step of our fluid/solid algorithm. Overall, the computational time to solve the projection step of our fluid/solid algorithm is similar to the time needed to solve the standard fluid-only projection step. The monolithic treatment results in a stable projection step, i.e. the kinetic energy does not increase in the projection step. Numerical results indicate that the method is second-order accurate in the L^∞-norm and demonstrate that its solutions agree quantitatively with experimental results.

Original language	English
Pages (from-to)	3246-3263
Number of pages	18
Journal	Journal of Computational Physics
Volume	231
Issue number	8
DOIs	https://doi.org/10.1016/j.jcp.2012.01.009
State	Published - 20 Apr 2012

Bibliographical note

Funding Information:
The research of F. Gibou was supported in part by ONR under grant agreement N00014–11-1–0027, by the National Science Foundation under grant agreement CHE 1027817, by the Department of Energy under grant agreement DE-FG02–08ER15991, by the Institute for Collaborative Biotechnologies through contract No. W911NF-09-D-0001 from the U.S. Army Research Office and by the W.M. Keck Foundation. The research of C. Min was supported in part by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010–0028298) and by the Korea Research Foundation Grant funded by the Korean Government (KRF-2011–0013649).

Keywords

Fluid
Interaction between fluid and solid
Level-set method
Navier-Stokes equations
Rigid body
Solid

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10.1016/j.jcp.2012.01.009

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title = "Efficient symmetric positive definite second-order accurate monolithic solver for fluid/solid interactions",

abstract = "We introduce a robust and efficient method to simulate strongly coupled (monolithic) fluid/rigid-body interactions. We take a fractional step approach, where the intermediate state variables of the fluid and of the solid are solved independently, before their interactions are enforced via a projection step. The projection step produces a symmetric positive definite linear system that can be efficiently solved using the preconditioned conjugate gradient method. In particular, we show how one can use the standard preconditioner used in standard fluid simulations to precondition the linear system associated with the projection step of our fluid/solid algorithm. Overall, the computational time to solve the projection step of our fluid/solid algorithm is similar to the time needed to solve the standard fluid-only projection step. The monolithic treatment results in a stable projection step, i.e. the kinetic energy does not increase in the projection step. Numerical results indicate that the method is second-order accurate in the L∞-norm and demonstrate that its solutions agree quantitatively with experimental results.",

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author = "Fr{\'e}d{\'e}ric Gibou and Chohong Min",

note = "Funding Information: The research of F. Gibou was supported in part by ONR under grant agreement N00014–11-1–0027, by the National Science Foundation under grant agreement CHE 1027817, by the Department of Energy under grant agreement DE-FG02–08ER15991, by the Institute for Collaborative Biotechnologies through contract No. W911NF-09-D-0001 from the U.S. Army Research Office and by the W.M. Keck Foundation. The research of C. Min was supported in part by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010–0028298) and by the Korea Research Foundation Grant funded by the Korean Government (KRF-2011–0013649).",

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N2 - We introduce a robust and efficient method to simulate strongly coupled (monolithic) fluid/rigid-body interactions. We take a fractional step approach, where the intermediate state variables of the fluid and of the solid are solved independently, before their interactions are enforced via a projection step. The projection step produces a symmetric positive definite linear system that can be efficiently solved using the preconditioned conjugate gradient method. In particular, we show how one can use the standard preconditioner used in standard fluid simulations to precondition the linear system associated with the projection step of our fluid/solid algorithm. Overall, the computational time to solve the projection step of our fluid/solid algorithm is similar to the time needed to solve the standard fluid-only projection step. The monolithic treatment results in a stable projection step, i.e. the kinetic energy does not increase in the projection step. Numerical results indicate that the method is second-order accurate in the L∞-norm and demonstrate that its solutions agree quantitatively with experimental results.

AB - We introduce a robust and efficient method to simulate strongly coupled (monolithic) fluid/rigid-body interactions. We take a fractional step approach, where the intermediate state variables of the fluid and of the solid are solved independently, before their interactions are enforced via a projection step. The projection step produces a symmetric positive definite linear system that can be efficiently solved using the preconditioned conjugate gradient method. In particular, we show how one can use the standard preconditioner used in standard fluid simulations to precondition the linear system associated with the projection step of our fluid/solid algorithm. Overall, the computational time to solve the projection step of our fluid/solid algorithm is similar to the time needed to solve the standard fluid-only projection step. The monolithic treatment results in a stable projection step, i.e. the kinetic energy does not increase in the projection step. Numerical results indicate that the method is second-order accurate in the L∞-norm and demonstrate that its solutions agree quantitatively with experimental results.

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Efficient symmetric positive definite second-order accurate monolithic solver for fluid/solid interactions

Abstract

Bibliographical note

Keywords

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