Title: Flowfield dependent variation method for one-dimensional stationary and moving boundary problems

Authors: Mohd Fadhli; Ashraf Ali Omar; Waqar Asrar

Addresses: Department of Mechanical Engineering, International Islamic University Malaysia, P.O. Box 10, Kuala Lumpur, 50728, Malaysia; Department of Aeronautical Engineering, University Tun Hussein Onn Malaysia, Parit Raja, Batu Pahat, Johor, 86400, Malaysia ' Department of Mechanical Engineering, International Islamic University Malaysia, P.O. Box 10, Kuala Lumpur, 50728, Malaysia ' Department of Mechanical Engineering, International Islamic University Malaysia, P.O. Box 10, Kuala Lumpur, 50728, Malaysia

Abstract: Complex fluid problems arise during fluid-structure interactions and pose a major challenge in the development of a stable generic numerical approach. Owing to the robustness of flowfield dependent variation (FDV) method in dealing with complex flow interactions, a new numerical procedure using the FDV method coupled with arbitrary Lagrangian-Eulerian (ALE) technique is developed. The combination of FDV and ALE method is discretised using finite volume method in order to give flexibility in dealing with complicated geometries. The formulation itself yields block tridiagonal matrix for one-dimensional formulation, which can then be solved using a relatively simple block lower-upper decomposition method. One-dimensional inviscid flows for stationary and moving boundary problems are solved using the proposed method. Stability criterion for stationary boundary problems has been derived. The method is found to be conditionally stable and its stability is dependent on the FDV parameters. Several numerical tests have been conducted and the results show good agreement with exact and available numerical solutions in the literature.

Keywords: flowfield dependent variation; FDV; arbitrary Lagrangian-Eulerian; ALE; moving boundary problems; stationary boundary problems; 1D boundary problems; fluid-structure interaction; FSI; finite volume method; inviscid flows; fluid flow.

DOI: 10.1504/IJCSE.2015.067071

International Journal of Computational Science and Engineering, 2015 Vol.10 No.1/2, pp.130 - 144

Received: 13 Sep 2013
Accepted: 17 Nov 2013

Published online: 25 Jan 2015 *

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