## One Solver for different Types of Flows

In order to compute a fluid flow a coupled system of partial differential equations (PDE's) has to be solved. In fluid mechanics one can characterize these PDE's according to the flow behavior they describe. These flow characteristics can be classified as parabolic, hyperbolic or elliptic. This classification was introduced by Smith (1978) and Hirsh (1989) and it prescribes an analogy between the type of the PDE and the type of the curves of second order. The classification provides a guide to appropriate initial and boundary conditions and to smoothness of the solutions.

This article shows the ability of our meshless CFD software ** NOGRID points **to simulate all these types of flows using one solver. In the following four figures only the material properties are different, the solver remains the same for all computations.

Figure 1: Water is flowing on steps: elliptic flow behavior (total time 3 s)

Figure 2: Honey is flowing on steps: parabolic flow behavior (total time 19 s)

Figure 3: Butter is falling down the steps: mixed flow behavior (total time 2.8 s)

Figure 4: A rubber is falling down the steps: hyperbolic flow behavior (total time 0.6 s)

Figure 1 shows a flow with a very small viscosity, like water. Thus the Reynolds number is huge. In figure 2 we computed the same case but we inserted a high viscosity (100 Pas). So in figure 2 the Reynolds number is very small (Re <<1). In figure 4 we computed not a flow but the displacements of a material with linear elastic material properties, like a rubber. The model used in figure 3 is a mixture of all implemented models and it could be characterized by visco-plastic material behavior.