A Meshfree Method for Simulations of Interactions between Fluids and Flexible Structures

A regularized Lagrangian finite point method for the simulation of incompressible viscous flows

“…The efficiency of FPM for solving a range of problems has been reported in [33][34][35][36][37]. In the same spirit of the finite point method, but using a Lagrangian description, Tiwari and Kuhnert have developed the Lagrangian finite point method (LFPM) and used it in many applications such as two-phase flows [38] and fluid-structure interactions [39]. Be a strong-form method, stabilization of FPM is often necessary.…”

“…Ellero et al [60] developed an alternative zero-density variation method by requiring that the volume of the fluid particles is constant and using Lagrangian multipliers to enforce the constrain. In LFPM [38,39], the Chorin's projection method [61] for solving the incompressible Navier-Stokers equation using grid-based methods is extended to the Lagrangian and meshless framework with the help of the weighted least squares method.…”

“…A Lagrangian finite point scheme similar to that proposed by Tiwari and Kuhnert [38,39] is applied to the projection method for the incompressible Navier-Stokes equations. The approximation of spatial derivatives is obtained by the weighted least squares method.…”

“…The approximation of spatial derivatives is obtained by the weighted least squares method. Different from the work of Tiwari and Kuhnert [38,39], the pressure Poisson equation with Neumann boundary condition is solved by a stabilized finite point method and the re-meshing technique is adopted to circumvent the problems associated with irregular particle distribution. Not like RSPH [48], the re-initialized particle distribution is not restricted to be uniform and the weighted least squares approximation is implemented to interpolate the properties of the old particles onto the new particle locations.…”

On the Truly Meshless Solution of Heat Conduction Problems in Heterogeneous Media

“…We noted that the finite point method is similar to the weighted least squares collocation method proposed by Sadat and Prax [4] for solving fluid flow and heat transfer problems. FPM has been applied and extended successfully to solve a range of problems including convective-diffusive transport [5], compressible flow [6], incompressible flow [7,8], potential flow [9], metal solidification [10], elasticity problems in structural mechanics [11], two-phase flows [12], and fluid-structure interactions [13]. Although quite successful in many applications, the extension and validation of FPM for problems involving heterogeneous media remains a big challenge [11].…”