Free surfaces in fluid mechanical systems are a great challenge for numerical simulation methods in themselves. However, many applications additionally exhibit moving structures interacting with the fluid. In most cases a realistic modeling with today's standard software is simply not feasible or would at least require a non economical amount of time and computational power to solve every-days simulation problems. One such example is the simulation of a boat being accelerated until it reaches its final inclination determined by its hull shape and its speed. A good understanding of this lifting process is mandatory for guiding the design and optimization of the hull. In grid-based methods such simulations are usually more simplified. Instead of allowing the boat moving freely during acceleration, the boat hull is entirely fixed or at most rotation around one axis is possible (thus reducing the degrees of freedom to zero or one), whereas the water flows with the velocity the boat should run with. This technique reduces computation time and numeric imprecision due to remeshing. It also gives a first insight into the fluid mechanical properties of the boat hull. However, it never provides the full information required for an in-depth understanding necessary in the design process. Rotational instabilities of a freely moving boat cannot be analyzed to name just one challenge.
Modeling abilities of NOGRID points
In contrast NOGRID points software, a meshless CFD (computational fluid dynamics) simulation software, based on FPM (Finite Pointset Method) permits several approaches for modeling the described scenario realistically. No restrictions on the movability of the boat are prescribed. In particular all six degrees of freedom, three for the velocity and three for the rotation of the rigid boat hull, are available. In the approach presented here the boat rests in a box partly filled with water. The boat hull is modeled as a set of faces which can freely move in the water. The fluid-structure interaction of the water with these faces is further determined by the center of gravity of the boat, by its mass and by its inertial tensor. Beginning at time t=0 an outer force and (small) torque is applied to the center of gravity (generated by the thrust of the propellers), and which now starts to accelerate the boat.
Figure 1: Accelerated boat with all six degrees of freedom
The role of finite points in NOGRID points
In NOGRID points finite points assume the role of the mesh used in FEM or FVM based methods. Beside the physical parameters of the model the user only has to determine the approximate density of these finite points. Tedious meshing and inaccurate and inefficient remeshing is not required since each finite point moves with the velocity of the fluid or (boat hull) face it belongs to. This Lagrangian view allows free surfaces and moving objects in a natural way. (It also allows directly utilizing the substantial derivatives in the Navier-Stokes equation, reducing the number of discrete derivatives to be computed and therefore increasing accuracy and efficiency.) For the boat model the exact flow of the water farther away from the boat hull is of no interest, hence a very sparse finite point density is chosen. In contrast, the water around the boat hull is resolved with high precision to allow an accurate computation of the lifting.
The finite point management is completely done by NOGRID points and is not visible to the user. At the beginning of the simulation finite points are inserted according to the prescribed finite point density until the fluid and the faces are completely filled out. If finite points move apart during the simulation and holes occur in the finite point cloud, additional finite points are automatically inserted. Similarly two finite points which have converged too close to each other are replaced by a single finite point. (It should be mentioned that such operations occur only scarcely and so do not compromise accuracy and efficiency as extensive remeshing and interpolation does in grid based methods.)
Figure 2: Accelerated boat with all six degrees of freedom
The simulated time is 11 seconds, the computation time of the simulation (done on a normal desktop computer equipped with a quad core processor) was about 15 hours. NOGRID points provides the means for economically support design and development in engineering, both drastically reducing time spent on preprocessing as well as computation time.
As mentioned above, further approaches are offered by the simulation abilities of NOGRID points providing an even more complete picture of the flow phenomena involved. These include the replacement of the explicit external force by a propeller, for example modeled by a small cylinder with a mass flow through the cylinder set to the mass flow generated by the propeller (computation time would increase only slightly). If required the propeller itself could be computed in detail.
If the boat is composed of a flexible structure where the elasticity of the hull influences the fluid dynamical behavior, the hull could be represented by a second phase with elastic material properties (which gives in fact a multi phase flow with a viscous and an elastic phase).