A coupled 3D isogeometric/least-square MPS approach for modeling fluid–structure interactions

Abstract

A two-way coupling method of the three-dimensional (3D) isogeometric approach and the least-square moving particle semi-implicit method (LSMPS) is presented for handling the fluid–structure interaction problems. This method takes advantages of isogeometric analysis (IGA) for structure deformation, e.g. the exact representation of the structure geometry and high accuracy for solution fields with relatively few elements, and that of the LSMPS method for fluid flow, e.g. its consistent discretization for both internal particles and boundary conditions. When the fluid is solved by the LSMPS method, the NURBS (Non-Uniform Rational B-Splines) surfaces provide boundary conditions for the LSMPS method. Afterward, the pressure on the NURBS surface is first evaluated from the pressure and the corresponding derivatives at the LSMPS particles by using the Taylor series expansion, and then integrated to determine the pressure force at the virtual points on the NURBS surface by using the Newton–Cotes method. Subsequently, the pressure forces at the virtual points are distributed onto the control nodes (i.e. control points) of the IGA elements so that the structure deformation can be analyzed by using the IGA method. The coupling algorithm is based on a Lagrangian framework and can handle the boundary conditions and the fluid–structure interactions accurately and easily. Finally, three examples, i.e. fluid flowing in a rigid pipe, fluid-tank, and fluid-torus interactions in the elastic regime, are simulated to demonstrate the accuracy and validity of the proposed coupling method.