Fabian Löschner, M.Sc.
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Email: loeschner@cs.rwth-aachen.de


Implicit Surface Tension for SPH Fluid Simulation

Stefan Rhys Jeske, Lukas Westhofen, Fabian Löschner, José Antonio Fernández-Fernández, Jan Bender
ACM Transactions on Graphics (TOG)

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)

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title = {Implicit {{Surface Tension}} for {{SPH Fluid Simulation}}},
author = {Jeske, Stefan Rhys and Westhofen, Lukas and L{\"o}schner, Fabian and {Fern{\'a}ndez-Fern{\'a}ndez}, Jos{\'e} Antonio and Bender, Jan},
year = {2023},
month = nov,
journal = {ACM Transactions on Graphics},
issn = {0730-0301},
doi = {10.1145/3631936},
urldate = {2023-11-07},
keywords = {adhesion,cohesion,fluid simulation,smoothed particle hydrodynamics,surface tension},

Micropolar Elasticity in Physically-Based Animation

Fabian Löschner, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Andreas Longva, Jan Bender
Proceedings of the ACM on Computer Graphics and Interactive Techniques (SCA)

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.

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author = {L\"{o}schner, Fabian and Fern\'{a}ndez-Fern\'{a}ndez, Jos\'{e} Antonio and Jeske, Stefan Rhys and Longva, Andreas and Bender, Jan},
title = {Micropolar Elasticity in Physically-Based Animation},
year = {2023},
issue_date = {August 2023},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {6},
number = {3},
url = {https://doi.org/10.1145/3606922},
doi = {10.1145/3606922},
journal = {Proceedings of the ACM on Computer Graphics and Interactive Techniques},
month = {aug},
articleno = {46},
numpages = {24}

Weighted Laplacian Smoothing for Surface Reconstruction of Particle-based Fluids

Fabian Löschner*, Timna Böttcher*, Stefan Rhys Jeske, Jan Bender
* joint first authors

Vision, Modeling and Visualization

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.

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@inproceedings {LBJB23,
booktitle = {Vision, Modeling, and Visualization},
title = {{Weighted Laplacian Smoothing for Surface Reconstruction of Particle-based Fluids}},
author = {Fabian L\"{o}schner and Timna B\"{o}ttcher and Stefan Rhys Jeske and Jan Bender},
year = {2023},
publisher = {The Eurographics Association},
ISBN = {978-3-03868-232-5},
DOI = {10.2312/vmv.20231245}

Fast Octree Neighborhood Search for SPH Simulations

José Antonio Fernández-Fernández, Lukas Westhofen, Fabian Löschner, Stefan Rhys Jeske, Andreas Longva, Jan Bender
ACM Transactions on Graphics (SIGGRAPH Asia 2022)

We present a new octree-based neighborhood search method for SPH simulation. A speedup of up to 1.9x is observed in comparison to state-of-the-art methods which rely on uniform grids. While our method focuses on maximizing performance in fixed-radius SPH simulations, we show that it can also be used in scenarios where the particle support radius is not constant thanks to the adaptive nature of the octree acceleration structure.

Neighborhood search methods typically consist of an acceleration structure that prunes the space of possible particle neighbor pairs, followed by direct distance comparisons between the remaining particle pairs. Previous works have focused on minimizing the number of comparisons. However, in an effort to minimize the actual computation time, we find that distance comparisons exhibit very high throughput on modern CPUs. By permitting more comparisons than strictly necessary, the time spent on preparing and searching the acceleration structure can be reduced, yielding a net positive speedup. The choice of an octree acceleration structure, instead of the uniform grid typically used in fixed-radius methods, ensures balanced computational tasks. This benefits both parallelism and provides consistently high computational intensity for the distance comparisons. We present a detailed account of high-level considerations that, together with low-level decisions, enable high throughput for performance-critical parts of the algorithm.

Finally, we demonstrate the high performance of our algorithm on a number of large-scale fixed-radius SPH benchmarks and show in experiments with a support radius ratio up to 3 that our method is also effective in multi-resolution SPH simulations.

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author= {Jos{\'{e}} Antonio Fern{\'{a}}ndez-Fern{\'{a}}ndez and Lukas Westhofen and Fabian L{\"{o}}schner and Stefan Rhys Jeske and Andreas Longva and Jan Bender },
title= {{Fast Octree Neighborhood Search for SPH Simulations}},
year= {2022},
journal= {ACM Transactions on Graphics (SIGGRAPH Asia)},
publisher= {ACM},
volume = {41},
number = {6},
pages= {13}

Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

Tassilo Kugelstadt, Jan Bender, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Fabian Löschner, Andreas Longva
Proceedings of the ACM on Computer Graphics and Interactive Techniques (Best Paper Award at SCA)

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [KKB2018] originally developed for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a state-of-the-art SPH simulator for elastic solids.

We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.

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author = {Kugelstadt, Tassilo and Bender, Jan and Fern{\'{a}}ndez-Fern{\'{a}}ndez, Jos{\'{e}} Antonio and Jeske, Stefan Rhys and L{\"{o}}schner, Fabian and Longva, Andreas},
title = {Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control},
year = {2021},
issue_date = {September 2021},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {4},
number = {3},
url = {https://doi.org/10.1145/3480142},
doi = {10.1145/3480142},
journal = {Proc. ACM Comput. Graph. Interact. Tech.},
month = sep,
articleno = {33},
numpages = {21},
keywords = {Smoothed Particle Hydrodynamics, fluid simulation, deformable solids, solid-fluid coupling}

Higher-Order Finite Elements for Embedded Simulation

Andreas Longva, Fabian Löschner, Tassilo Kugelstadt, José Antonio Fernández-Fernández, Jan Bender
ACM Transactions on Graphics (SIGGRAPH Asia 2020)

As demands for high-fidelity physics-based animations increase, the need for accurate methods for simulating deformable solids grows. While higher-order finite elements are commonplace in engineering due to their superior approximation properties for many problems, they have gained little traction in the computer graphics community. This may partially be explained by the need for finite element meshes to approximate the highly complex geometry of models used in graphics applications. Due to the additional per-element computational expense of higher-order elements, larger elements are needed, and the error incurred due to the geometry mismatch eradicates the benefits of higher-order discretizations. One solution to this problem is the embedding of the geometry into a coarser finite element mesh. However, to date there is no adequate, practical computational framework that permits the accurate embedding into higher-order elements.

We develop a novel, robust quadrature generation method that generates theoretically guaranteed high-quality sub-cell integration rules of arbitrary polynomial accuracy. The number of quadrature points generated is bounded only by the desired degree of the polynomial, independent of the embedded geometry. Additionally, we build on recent work in the Finite Cell Method (FCM) community so as to tackle the severe ill-conditioning caused by partially filled elements by adapting an Additive-Schwarz-based preconditioner so that it is suitable for use with state-of-the-art non-linear material models from the graphics literature. Together these two contributions constitute a general-purpose framework for embedded simulation with higher-order finite elements.

We finally demonstrate the benefits of our framework in several scenarios, in which second-order hexahedra and tetrahedra clearly outperform their first-order counterparts.

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author= {Andreas Longva and Fabian L{\"{o}}schner and Tassilo Kugelstadt and Jos{\'{e}} Antonio Fern{\'{a}}ndez-Fern{\'{a}}ndez and Jan Bender },
title= {{Higher-Order Finite Elements for Embedded Simulation}},
year= {2020},
journal= {ACM Transactions on Graphics (SIGGRAPH Asia)},
publisher= {ACM},
volume = {39},
number = {6},
pages= {14}

Higher-Order Time Integration for Deformable Solids

Fabian Löschner, Andreas Longva, Stefan Rhys Jeske, Tassilo Kugelstadt, Jan Bender
Computer Graphics Forum

Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first-order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second-order methods, their use is not widespread. Many of these well-known methods have significant drawbacks such as severe numerical damping or scene-dependent time step restrictions to ensure stability. In this paper, we discuss the most relevant requirements on such methods in computer animation and motivate the interest beyond first-order accuracy. Keeping these requirements in mind, we investigate several promising methods from the families of diagonally implicit Runge-Kutta (DIRK) and Rosenbrock methods which currently do not appear to have considerable popularity in this field. We show that the usage of such methods improves the visual quality of physical animations. In addition, we demonstrate that they allow distinctly more control over damping at lower computational cost than classical methods. As part of our theoretical contribution, we review aspects of simulations that are often considered more intricate with higher-order methods, such as contact handling. To this end, we derive an implicit linearized contact model based on a predictor-corrector approach that leads to consistent behavior with higher-order integrators as predictors. Our contact model is well suited for the simulation of stiff, nonlinear materials with the integration methods presented in this paper and more common methods such as Backward Euler alike.

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author = {Fabian L{\"{o}}schner and Andreas Longva and Stefan Jeske and Tassilo Kugelstadt and Jan Bender},
title = {Higher-Order Time Integration for Deformable Solids},
year = {2020},
journal = {Computer Graphics Forum},
volume = {39},
number = {8}

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