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

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.