Implicit second-order CUSP gridless method for unsteady moving boundary simulations

Abstract

Efficient first-order and second-order gridless method is presented for calculation of unsteady compressible flows. The convective upwind split pressure (CUSP) gridless scheme is applied for solving unsteady fluid flow equations in the arbitrary Lagrangian–Eulerian (ALE) formulation. In order to manage dynamic cloud and nodes movement, the nodes are moved based on the boundary movements using the segment spring analogy. Discretization of spatial derivatives are done by using the Taylor series least squares at each node. For increasing the accuracy, second-order Taylor series (SOTS) expansion is also used on the CUSP gridless method. For time advancement, implicit dual-time and explicit schemes are used. The accuracy of the methods is compared with the AGARD experimental data and finite volume results for some test cases in steady and unsteady flows. Results show that the CUSP gridless scheme is accurate in steady and unsteady flows and using the second-order discretization increases the accuracy a little bit and also the gridless schemes reduce the computational time as compared with finite volume method. Numerical results are in good agreement with the experimental data.