Hamiltonian structure of CIVA-particle method in two-dimensional passive scalar advection problem

摘要

This paper presents improvement of the CIVA-based Lagrangian mesh-free method, namely the CIVA-particle method, for CFD. CIVA is a flexible, accurate and stable interpolation method, which extends the CIP method for mesh-free methods based on N-simplex and barycentric coordinates. However, the CIVA-particle method with the conventional time integrators is subject to problems in that the invariants of the system are not preserved in a long-time computation. In order to solve the problems, symplectic time integrators are applied in this study.