A geometrical scan-sphere test is optionally performed to verify that points are on the point–cloud boundary. Since accurate and fast discrete versions of the operator are not straightforward to implement in meshless context, the technique exploits favourable properties of a discrete Laplacian that handles highly irregular arrangements of points. A technique for detecting the edge or boundary of a point cloud is introduced, which is based on the Laplacian properties for detecting jumps. The advection adjusts to moving or deforming boundaries, and volume-conservation is enforced by solving a set of geometrical constraints. Poisson Pressure Equation (PPE) formulation of Navier-Stokes equations is discretised in Lagrangian context using recently introduced spatial operators based on finite differences. A Lagrangian meshless method is introduced for numerical simulation of flows of incompressible fluids with free surface.
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