meshless methods

The simulation of nonlinear surface waves is of significant importance in safety studies of fluid containers and reservoirs. In this paper, nonlinear free surface flows are simulated using a fixed grid method which employs local exponential basis functions (EBFs). Assuming the flow to be inviscid and irrotational, the velocity potential Laplace’s equation is spatially discretized and solved by considering the nonlinear Bernoulli’s equation for irrotational flow as the boundary condition on the free surface. The nonlinear boundary conditions are imposed through a semi-implicit iterative time marching. The fixed grid feature of the method, based on a Lagrangian description of fluid flow, allows for retaining the portion of the discretization performed in the first time step for the bulk of the fluid. Thus, the portion which pertains to the regions near the moving boundaries is reprocessed during the time marching.  The accuracy and efficiency of the existing solution is shown by simulating various problems such as liquid sloshing induced by external excitation of the reservoir or initial deformed shape of liquid, seiche phenomena and solitary wave propagation in a basin with constant depth or with a step, and comparing the results with those which are analytically available or those from available codes such as Abaqus.  The proposed method shows far better stability of the results when compared with those of Abaqus which sometimes exhibit divergence after a relatively large number of time steps. For instance, in the propagation of the considered solitary wave in an infinite-like domain problem, the wave height is calculated by the maximum error of 1.6% and 9% using the present method and Abaqus, respectively.