TY - JOUR

T1 - An implicit algorithm within the arbitrary Lagrangian-Eulerian formulation for solving incompressible fluid flow with large boundary motions

AU - Filipovic, Nenad

AU - Mijailovic, Srboljub

AU - Tsuda, Akira

AU - Kojic, Milos

PY - 2006/9/15

Y1 - 2006/9/15

N2 - The objective of the paper is to present an implicit algorithm for incompressible fluid flow solution using the arbitrary Lagrangian-Eulerian (ALE) formulation and to investigate solution accuracy and stability of the algorithm. The governing equations of the implicit procedure are derived using isoparametric interpolations for the fluid velocities and pressure. The details suitable for general use are presented in our derivations of the fundamental equations and of the basic finite element balance equations. The penalty method is utilized to eliminate the pressure on the element level. Accuracy and stability of the solutions are demonstrated in three examples for which the analytical solutions are known. In the first example, the Burger's equation analogue to 1-D fluid flows is solved without and with FE mesh motion, to show that the mesh motion practically does not affect the solutions. In the second example, the solitary wave motion with large displacements of the free boundary is solved as a benchmark problem. In the third example, the fluid flow in an infinite contractible and expandable pipe with prescribed large radial wall motion is solved. This example is specifically attractive for biological flows as in blood vessels and lung airways. All solutions presented show that the proposed algorithm is sufficiently accurate and stable. Since the algorithm is implicit, high accuracy of results can be achieved with a relatively large time step.

AB - The objective of the paper is to present an implicit algorithm for incompressible fluid flow solution using the arbitrary Lagrangian-Eulerian (ALE) formulation and to investigate solution accuracy and stability of the algorithm. The governing equations of the implicit procedure are derived using isoparametric interpolations for the fluid velocities and pressure. The details suitable for general use are presented in our derivations of the fundamental equations and of the basic finite element balance equations. The penalty method is utilized to eliminate the pressure on the element level. Accuracy and stability of the solutions are demonstrated in three examples for which the analytical solutions are known. In the first example, the Burger's equation analogue to 1-D fluid flows is solved without and with FE mesh motion, to show that the mesh motion practically does not affect the solutions. In the second example, the solitary wave motion with large displacements of the free boundary is solved as a benchmark problem. In the third example, the fluid flow in an infinite contractible and expandable pipe with prescribed large radial wall motion is solved. This example is specifically attractive for biological flows as in blood vessels and lung airways. All solutions presented show that the proposed algorithm is sufficiently accurate and stable. Since the algorithm is implicit, high accuracy of results can be achieved with a relatively large time step.

KW - ALE formulation

KW - Implicit algorithm

KW - Incompressible viscous fluid flow

KW - Large boundary motion

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U2 - 10.1016/j.cma.2005.12.009

DO - 10.1016/j.cma.2005.12.009

M3 - Article

AN - SCOPUS:33745945240

VL - 195

SP - 6347

EP - 6361

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 44-47

ER -