An Unstructured hp Finite-Element Scheme for Fluid Flow and Heat Transfer in Moving Domains

This paper presents the formulation, validation, and application of a spectral/hp algorithm for numerical solution of the Navier–Stokes and heat/scalar transport equations in arbitrarily moving complex geometries. The new spectral element algorithm is based on the arbitrary Lagrangian Eulerian formulation and utilizes modal expansion of Jacobi polynomials in mixed triangular and quadrilateral elements in two dimensions. Time integration is performed by stiffly stable schemes and can deliver up to third-order time accuracy for transient problems. Test cases with sufficiently smooth solutions demonstrate spectral convergence and low phase/dissipation error. Preliminary simulation results for micro-mixers and micro-heat spreaders are also presented.