We present a novel approach to fluid simulation, allowing us to take into account the surface energy in a precise manner. This new approach combines a novel, topology-adaptive approach to deformable interface tracking, called the deformable simplicial complexes method (DSC) with an optimization-based, linear finite element method for solving the incompressible Euler equations. The deformable simplicial complexes track the surface of the fluid: the fluid-air interface is represented explicitly as a piecewise linear surface which is a subset of tetrahedralization of the space, such that the interface can be also represented implicitly as a set of faces separating tetrahedra marked as inside from the ones marked as outside. This representation introduces insignificant and controllable numerical diffusion, allows robust topological adaptivity and provides both a volumetric finite element mesh for solving the fluid dynamics equations as well as direct access to the interface geometry data, making inclusion of a new surface energy term feasible. Furthermore, using an unstructured mesh makes it straightforward to handle curved solid boundaries and gives us a possibility to explore several fluid-solid interaction scenarios.
Month: January 2011
Langevin Particle: A Self-Adaptive Lagrangian Primitive For Flow Simulation Enhancement
We develop a new Lagrangian primitive, named Langevin particle, to incorporate turbulent flow details in fluid simulation. A group of the particles are distributed inside the simulation domain based on a turbulence energy model with turbulence viscosity. A particle in particular moves obeying the generalized Langevin equation, a well-known stochastic differential equation that describes the particle’s motion as a random Markov process. The resultant particle trajectory shows self-adapted fluctuation in accordance to the turbulence energy, while following the global flow dynamics. We then feed back Langevin forces to the simulation based on the stochastic trajectory, which drive the flow with necessary turbulence. The new hybrid flow simulation method features nonrestricted particle evolution requiring minimal extra manipulation after initiation. The flow turbulence is easily controlled and the total computational overhead of enhancement is minimal based on typical fluid solvers.
Langevin Particle: A Self-Adaptive Lagrangian Primitive For Flow Simulation Enhancement
PhD Thesis
Cem Yuksel, Texas A&M, 2010: Real-Time Water Waves with Wave Particles
Hybrid Multiresolution Wire
We describe a method for the visual interactive simulation of wires contacting with rigid multibodies. The physical model used is a hybrid combining lumped elements and massless quasistatic representations. The latter is based on a kinematic constraint preserving the total length of the wire along a segmented path which can involve multiple bodies simultaneously and dry frictional contact nodes used for roping, lassoing and fastening. These nodes provide stick and slide friction along edges of the contacting geometries. The lumped element resolution is adapted dynamically based on local stability criteria, becoming coarser as the tension increases, and up to the purely kinematic representation. Kinematic segments and contact nodes are added and deleted and propagated based on contact geometries and dry friction configurations. The method gives dramatic increase on both performance and robustness because it quickly decimates superfluous nodes without loosing stability, yet adapts to complex configurations with many contacts and high curvature, keeping a fixed, large integration time step. Numerical results demonstrating the performance and stability of the adaptive multiresolution scheme are presented along with an array of representative simulation examples illustrating the versatility of the frictional contact model.
Constraint Fluids
We present a fluid simulation method based on Smoothed Particle Hydrodynamics (SPH) in which incompressibility and boundary conditions are enforced using holonomic kinematic constraints on the density. This formulation enables systematic multiphysics integration in which interactions are modeled via similar constraints between the fluid pseudo-particles and impenetrable surfaces of other bodies. These conditions embody Archimede’s principle for solids and thus buoyancy results as a direct consequence. We use a variational time stepping scheme suitable for general constrained multibody systems we call SPOOK. Each step requires the solution of only one Mixed Linear Complementarity Problem (MLCP) with very few inequalities, corresponding to solid boundary conditions. We solve this MLCP with a fast iterative method. Overall stability is vastly improved in comparison to the unconstrained version of SPH, and this allows much larger time steps, and an increase in overall performance by two orders of magnitude. Proof of concept is given for computer graphics applications and interactive simulations.