# MESHLESS MODELING AND SIMULATION

Numerical fluid mechanics (Computational Fluid Dynamics, CFD) is a well known and established method within fluid mechanics and is used to solve fluid mechanical problems approximately with numerical methods. The model equations are the Navier-Stokes equations, which are nonlinear partial differential equations of second order, which prescribe a fluid completely.
An important step in handling partial differential equations is to use discrete algebraic replacements for the continuous differential equations. Several methods are currently in use, such as the finite volume (FV), finite element (FE), and finite difference (FD) method. We use a general finite difference (gFD) method to discretize the Navier-Stokes equation. General means that we operate on an unstructured points basis, whereas the classical FD-method operates on structured points only. Figure 1: On the left side a point cloud is used to discretize the domain, on the right side a FEM mesh is used

Our meshless CFD software NOGRID points, as well as NOGRID pointsBlow,  is based on FPM (Finite Pointset Method), a method, which generates a local defined, non-stationary point cloud distribution for discretization of the Navier-Stokes equations. The FPM method itself is based on the general finite difference method and the key features are:

• Instead of a mesh FPM discretizes the continuum domain by a point cloud
• The point density is prescribed by a smoothing length defined locally and can vary from one time step to another
• FPM does not use a rigid neighborhood list for a certain point (=node) as it is required in a mesh based method. All neighbors are allowed to move and the neighborhood list is recomputed each time step

Thus, the simple idea of the NOGRID method is to use a dynamical discretization method. The following video shows how simple it is to compute a certain CFD task:

Video 1: Creating and computing a simple 2-D channel flow with a tube inside the domain

The point cloud is generated automatically by the software depending on users settings. That's why there is no need to generate a mesh as required in classical CFD methods. FPM points are automatically filled, moved, refilled and cleaned depending on user specifications. The point cloud can be defined variously, e.g. constant in the whole flow domain, changing with time or increasing/decreasing locally depending on the flow/geometry situation.   Figure 2: 3D-Modelling with NOGRID's COMPASS: No volume mesh is required, only a surface mesh is used as replacement for the CAD representation   Figure 3: NOGRID points reads the CAD geometry file and the user can start the computation immediately if all conditions are given

The main advantages of NOGRID's CFD software are:

• Easy modeling of all free surface problems
• Simple representation of multiphase flows within NOGRID points
• Natural interface for the description of moving parts and boundaries
• Straightforward solutions for Fluid Structure Interaction (FSI) tasks
• Very short computation time in comparison to classical methods without reducing results quality
• Direct import of models from your CAD system without mesh generation