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An immersed boundary projection method for solving the fluid-rigid body interaction problems

Published: 01 October 2022 Publication History

Abstract

We develop an immersed boundary projection method for solving the Naiver-Stokes equations and Newton-Euler equations to simulate the fluid-rigid body interactions in two and three dimensions. A novel fractional step algorithm is introduced for which fast solvers can be applied by exploiting the algebraic structure of the underlying schemes. The Navier-Stokes equations are decoupled while the Newton-Euler equations are solved simultaneously with a constraint equation of the immersed boundary force density. In contrast to previous works, the present method preserves both the fluid incompressibility and the kinematic constraint of the rigid body dynamics at a discrete level simultaneously while maintaining numerical stability. We demonstrate the numerical results of the present method involving spherical and spheroidal rigid bodies with a moderate range of density ratios, which are congruent with the results in the literature.

Highlights

A novel immersed boundary projection method for simulating the fluid-rigid body interactions.
Fluid incompressibility and no-slip boundary condition are satisfied simultaneously.
A constraint equation for the immersed boundary force components is derived.
Numerical stability is maintained in the limit of density ratio of unity.
Matrix-free algorithm for which FFT-based fast solvers can be readily applied.

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            Published In

            cover image Journal of Computational Physics
            Journal of Computational Physics  Volume 466, Issue C
            Oct 2022
            1032 pages

            Publisher

            Academic Press Professional, Inc.

            United States

            Publication History

            Published: 01 October 2022

            Author Tags

            1. Immersed boundary projection method
            2. Fluid-rigid body interactions
            3. Fractional step method
            4. Cauchy's stress theorem
            5. Rigid body dynamics

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