Tassilo Kugelstadt, M.Sc.|
In this paper we introduce a novel micropolar material model for the simulation of turbulent inviscid fluids. The governing equations are solved by using the concept of Smoothed Particle Hydrodynamics (SPH). As already investigated in previous works, SPH fluid simulations suffer from numerical diffusion which leads to a lower vorticity, a loss in turbulent details and finally in less realistic results. To solve this problem we propose a micropolar fluid model. The micropolar fluid model is a generalization of the classical Navier-Stokes equations, which are typically used in computer graphics to simulate fluids. In contrast to the classical Navier-Stokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. In addition to the linear velocity field these fluids also have a field of microrotation which represents existing vortices and provides a source for new ones. However, classical micropolar materials are viscous and the translational and the rotational motion are coupled in a dissipative way. Since our goal is to simulate turbulent fluids, we introduce a novel modified micropolar material for inviscid fluids with a non-dissipative coupling. Our model can generate realistic turbulences, is linear and angular momentum conserving, can be easily integrated in existing SPH simulation methods and its computational overhead is negligible.
We present a novel method to simulate bending and torsion of elastic rods within the position-based dynamics (PBD) framework. The main challenge is that torsion effects of Cosserat rods are described in terms of material frames which are attached to the centerline of the rod. But frames or orientations do not fit into the classical position-based dynamics formulation. To solve this problem we introduce new types of constraints to couple orientations which are represented by unit quaternions. For constraint projection quaternions are treated in the exact same way as positions. Unit length is enforced with an additional constraint. This allows us to use the strain measures form Cosserat theory directly as constraints in PBD. It leads to very simple algebraic expressions for the correction displacements which only contain quaternion products and additions. Our results show that our method is very robust and accurately produces the complex bending and torsion effects of rods. Due to its simplicity our method is very efficient and more than one order of magnitude faster than existing position-based rod simulation methods. It even achieves the same performance as position-based simulations without torsion effects.