Topology optimization for fluid flows using the MPS method incorporating the level set method

Topology optimization for fluid field problems has been studied for many years, but most of them use the Eulerian coordinate system in the numerical analysis methods such as the finite element method and the finite volume method. The moving particle semi-implicit (MPS) method is one of the particle methods, which can be used to analyze incompressible free surface fluid flows. The MPS method is a meshless method based on the Lagrangian coordinate system without surface tracking by a mesh or a scalar quantity. It has attracted attention in recent years since this has several advantages such as the easy expression of the free boundaries. This paper presents a new topology optimization method for fluid dynamics problems using the MPS method. First, the optimization problems are formulated based on the level set method and the MPS method. Next, the design sensitivities are derived using the Lagrange multiplier method and adjoint variable method. The optimization algorithm is constructed based on those formulations, and the validity and the availability of the proposed method are confirmed through several numerical examples