In this research, a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries. A Lagrangian formulation established on pressure, as a potential equation, is employed. In this method, the approximate solution is expressed by a local linear combination of exponential basis functions (EBFs), with complex-valued exponents, satisfying the governing equation within subdomains. The compatibility between the subdomains is weakly satisfied through the minimization of a suitable norm written on the residuals of the continuity conditions. The numerical solution is performed in a time marching approach using an implicit algorithm. The use of EBFs helps to find nodal velocities with high accuracy leading to a precise geometry updating. The developed Lagrangian meshless algorithm is applied to variety of linear and nonlinear benchmark problems. Non-linear sloshing fluids in rigid rectangular two-dimensional basins are particularly addressed. Also, another Lagrangian algorithm based on velocity potential is represented using this new local meshless method. In this part, a fix grid method is developed that fluid boundaries are moved only. So more disturbed surfaces may be simulated with this approach. More benchmark problems (for example dam break problem) are simulated using velocity potential. Simulations show that the presented time marching with the new meshless method based on local EBFs give accurate results that have good agreement with analytical and experimental data. Key Words Free surface flow, Lagrangian approach, Numerical simulation, Velocity potential, Nonlinear sloshing, and Dam break problem.
