Regular Article: Free-Surface Flow Simulation Using hp/Spectral Elements

Computational instabilities inherent in the solution of inviscid, incompressible free-surface flow have been apparent for some time and different techniques have been used to overcome them. In this paper we attempt to explain why these instabilities occur and in doing so, a method is developed to study the spatially semi-discrete eigenvalues and eigenvectors which govern the stability of the system. It is found that the asymmetric spatial discretisation of the fluid domain causes the instabilities. After mechanisms for stability are recognised and implemented, unsteady, inviscid, incompressible, linear and non-linear free-surface flow is simulated using a hp/spectral element code, ensuring fast convergence, which incorporates arbitrary Lagrangian-Eulerian (ALE) techniques to decrease deformation of the computational mesh.

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