Publications

The numerical simulation of surface tension is an active area of research in many different fields of application and has been attempted using a wide range of methods. Our contribution is the derivation and implementation of an implicit cohesion force based approach for the simulation of surface tension effects using the Smoothed Particle Hydrodynamics (SPH) method. We define a continuous formulation inspired by the properties of surface tension at the molecular scale which is spatially discretized using SPH. An adapted variant of the linearized backward Euler method is used for time discretization, which we also strongly couple with an implicit viscosity model. Finally, we extend our formulation with adhesion forces for interfaces with rigid objects.

Existing SPH approaches for surface tension in computer graphics are mostly based on explicit time integration, thereby lacking in stability for challenging settings. We compare our implicit surface tension method to these approaches and further evaluate our model on a wider variety of complex scenarios, showcasing its efficacy and versatility. Among others, these include but are not limited to simulations of a water crown, a dripping faucet and a droplet-toy.

Paper (ACM, Free of Charge)

We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material's strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We propose a new orthotropic micropolar curvature energy that allows us to make materials stiff to bending in specific directions.

For the simulation of dynamic micropolar deformables we propose a novel incremental potential formulation with a consistent FEM discretization that is well suited for the use in physically-based animation. This allows us to easily couple micropolar deformables with dynamic collisions through a contact model inspired from the Incremental Potential Contact (IPC) approach. For the spatial discretization with FEM we discuss the challenges related to the rotational degrees of freedom and propose a scheme based on the interpolation of angular velocities followed by quaternion time integration at the quadrature points.

In our evaluation we validate the consistency and accuracy of our discretization approach and demonstrate several compelling use cases for micropolar materials. This includes explicit control over bending and torsion stiffness, deformation through prescription of a volumetric curvature field and robust interaction of micropolar deformables with dynamic collisions.

A well-known issue with the widely used Smoothed Particle Hydrodynamics (SPH) method is the neighborhood deficiency. Near the surface, the SPH interpolant fails to accurately capture the underlying fields due to a lack of neighboring particles. These errors may introduce ghost forces or other visual artifacts into the simulation.

In this work we investigate three different popular methods to correct the first-order spatial derivative SPH operators up to linear accuracy, namely the Kernel Gradient Correction (KGC), Moving Least Squares (MLS) and Reproducing Kernel Particle Method (RKPM). We provide a thorough, theoretical comparison in which we remark strong resemblance between the aforementioned methods. We support this by an analysis using synthetic test scenarios. Additionally, we apply the correction methods in simulations with boundary handling, viscosity, surface tension, vorticity and elastic solids to showcase the reduction or elimination of common numerical artifacts like ghost forces. Lastly, we show that incorporating the correction algorithms in a state-of-the-art SPH solver only incurs a negligible reduction in computational performance.

A common way to handle boundaries in SPH fluid simulations is to sample the surface of the boundary geometry using particles. These boundary particles are assigned the same properties as the fluid particles and are considered in the pressure force computation to avoid a penetration of the boundary. However, the pressure solver requires a pressure value for each particle. These are typically not computed for the boundary particles due to the computational overhead. Therefore, several strategies have been investigated in previous works to obtain boundary pressure values. A popular, simple technique is pressure mirroring, which mirrors the values from the fluid particles. This method is efficient, but may cause visual artifacts. More complex approaches like pressure extrapolation aim to avoid these artifacts at the cost of computation time.

We introduce a constraint-based derivation of Divergence-Free SPH (DFSPH) --- a common state-of-the-art pressure solver. This derivation gives us new insights on how to integrate boundary particles in the pressure solve without the need of explicitly computing boundary pressure values. This yields a more elegant formulation of the pressure solver that avoids the aforementioned problems.

In physically-based animation, producing detailed and realistic surface reconstructions for rendering is an important part of a simulation pipeline for particle-based fluids. In this paper we propose a post-processing approach to obtain smooth surfaces from "blobby" marching cubes triangulations without visual volume loss or shrinkage of drops and splashes. In contrast to other state-of-the-art methods that often require changes to the entire reconstruction pipeline our approach is easy to implement and less computationally expensive.

The main component is Laplacian mesh smoothing with our proposed feature weights that dampen the smoothing in regions of the mesh with splashes and isolated particles without reducing effectiveness in regions that are supposed to be flat. In addition, we suggest a specialized decimation procedure to avoid artifacts due to low-quality triangle configurations generated by marching cubes and a normal smoothing pass to further increase quality when visualizing the mesh with physically-based rendering. For improved computational efficiency of the method, we outline the option of integrating computation of our weights into an existing reconstruction pipeline as most involved quantities are already known during reconstruction. Finally, we evaluate our post-processing implementation on high-resolution smoothed particle hydrodynamics (SPH) simulations.

The properties of thermally sprayed coatings depend heavily on their microstructure. The microstructure is determined by the dynamics of the impact of the droplets on the substrate surface and the subsequent overlapping of the previously solidified and deformed droplets. Substrate preparation prior to spraying ensures strong adhesion of the coating. This includes roughening and preheating of the substrate surface. In the present study, the smoothed particle hydrodynamics (SPH) method is used to model the Al2O3 impact on a preheated substrate and a roughened substrate surface. A semi-implicit enthalpy–porosity method is applied to simulate the solidification process in the mushy zone. In addition, an implicit correction for SPH simulations is used to improve the performance and stability of the simulation. To investigate the dynamics of heat transfer in the contact between the surface and the droplet, the discretization of the substrate is also taken into account. The results show that the studied substrate surface conditions affect the splat morphology and the solidification process. Subsequently, the simulation of multiple droplets for coating formation is also performed and analyzed.