Year: Author:

Marcel Weiler, Dan Koschier, Magnus Brand, Jan Bender
Computer Graphics Forum (Eurographics)

In this paper, we present a novel physically consistent implicit solver for the simulation of highly viscous fluids using the Smoothed Particle Hydrodynamics (SPH) formalism. Our method is the result of a theoretical and practical in-depth analysis of the most recent implicit SPH solvers for viscous materials. Based on our findings, we developed a list of requirements that are vital to produce a realistic motion of a viscous fluid. These essential requirements include momentum conservation, a physically meaningful behavior under temporal and spatial refinement, the absence of ghost forces induced by spurious viscosities and the ability to reproduce complex physical effects that can be observed in nature. On the basis of several theoretical analyses, quantitative academic comparisons and complex visual experiments we show that none of the recent approaches is able to satisfy all requirements. In contrast, our proposed method meets all demands and therefore produces realistic animations in highly complex scenarios. We demonstrate that our solver outperforms former approaches in terms of physical accuracy and memory consumption while it is comparable in terms of computational performance. In addition to the implicit viscosity solver, we present a method to simulate melting objects. Therefore, we generalize the viscosity model to a spatially varying viscosity field and provide an SPH discretization of the heat equation.

» Show BibTeX

author = {Marcel Weiler and Dan Koschier and Magnus Brand and Jan Bender},
title = {A Physically Consistent Implicit Viscosity Solver for SPH Fluids},
year = {2018},
journal = {Computer Graphics Forum (Eurographics)},
volume = {37},
number = {2}

Crispin Deul, Tassilo Kugelstadt, Marcel Weiler, Jan Bender
Computer Graphics Forum

In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the Position-Based Dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of non-linear equations using a non-linear Gauss-Seidel solver. However, this solver requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast we use Newton iterations in combination with our direct solver to solve the non-linear equations which significantly improves convergence by solving all constraints of an acyclic structure (tree), simultaneously. Our solver only requires a few Newton iterations to achieve high stiffness and inextensibility. We model inextensible rods and trees using rigid segments connected by constraints. Bending and twisting constraints are derived from the well-established Cosserat model. The high performance of our solver is demonstrated in highly realistic simulations of rods consisting of multiple ten-thousand segments. In summary, our method allows the efficient simulation of stiff rods in the Position-Based Dynamics framework with a speedup of two orders of magnitude compared to the original XPBD approach.

» Show BibTeX

author = {Crispin Deul and Tassilo Kugelstadt and Marcel Weiler and Jan Bender},
title = {Direct Position-Based Solver for Stiff Rods},
year = {2018},
journal = {Computer Graphics Forum}

Jens Cornelis, Jan Bender, Christoph Gissler, Markus Ihmsen, Matthias Teschner
The Visual Computer

Incompressible SPH (ISPH) is a promising concept for the pressure computation in SPH. It works with large timesteps and the underlying pressure Poisson equation (PPE) can be solved very efficiently. Still, various aspects of current ISPH formulations can be optimized.

This paper discusses issues of the two standard source terms that are typically employed in PPEs, i.e. density invariance (DI) and velocity divergence (VD). We show that the DI source term suffers from significant artificial viscosity, while the VD source term suffers from particle disorder and volume loss.

As a conclusion of these findings, we propose a novel source term handling. A first PPE is solved with the VD source term to compute a divergence-free velocity field with minimized artificial viscosity. To address the resulting volume error and particle disorder, a second PPE is solved to improve the sampling quality. The result of the second PPE is used for a particle shift (PS) only. The divergence-free velocity field - computed from the first PPE - is not changed, but only resampled at the updated particle positions. Thus, the proposed source term handling incorporates velocity divergence and particle shift (VD+PS).

» Show BibTeX

author = {Cornelis, Jens and Bender, Jan and Gissler, Christoph and Ihmsen, Markus and Teschner, Matthias},
title = {An optimized source term formulation for incompressible SPH},
journal = {The Visual Computer},
year = {2018},
month = {Feb},
issn = {1432-2315},
day = {20},
doi = {10.1007/s00371-018-1488-8},
url = {},

Previous Year (2017)
Disclaimer Home Visual Computing institute RWTH Aachen University