A novel implicit meshless particle method: NURBS-based particle hydrodynamics (NBPH)

In this work, a new strong form-based implicit meshless particle method, NURBS based Particle Hydrodynamics (NBPH) is proposed. The kernel approximation is replaced by NURBS basis function interpolation. Thus, the calculation of physical field function relies on NURBS basis function-based interpolation, rather than weighted contributions from neighboring particles. Pseudo particles and real particles are configured in the algorithm to accomplish the physical field solution and geometry description. And the gradient operators and Laplacian operators are evaluated based on the partial derivatives of the NURBS basis functions combined with control variables. The update of the physical field functions is completed by an implicit time integration without pre-setting more constraints or intermediate intervention. Generally, the number of pseudo particles is less than the number of real particles, and the value of this difference is related to the order of NURBS basis functions. In addition, surface tension is achieved by cohesion and surface area minimization, tensile instability is solved by shifting particles. Based on the good performance of NBPH in solving numerical simulations of transient conduction and several incompressible flows, it is demonstrated that NBPH is a feasible meshless method. The proposed NBPH scheme provides an alternative computer method for nonlinear transient analysis, such as transient heat transfer and incompressible flow simulation in engineering.