The efficient simulation of incompressible fluids remains a difficult and open problem. Prior works often make various tradeoffs between incompressibility, stability, and cost. Yet, it is rare to obtain all three. In this paper, we introduce a novel incompressible Smoothed Particle Hydrodynamics (SPH) scheme which uses a second-order implicit descent scheme to optimize a variational energy specially formulated to approach incompressibility. We demonstrate that our method is superior in both incompressibility and stability with a minimal cost to computational budget. Furthermore, we demonstrate that our method is unconditionally stable even under extreme time steps, making it suitable for interactive applications.

Vertex Block Descent is a fast physics-based simulation method that is unconditionally stable, highly parallelizable, and capable of converging to the implicit Euler solution. We extend it using an augmented Lagrangian formulation to address some of its fundamental limitations. First, we introduce a mechanism to handle hard constraints with infinite stiffness without introducing numerical instabilities. Second, we substantially improve the convergence in the presence of high stiffness ratios. These changes we introduce allow simulating complex contact scenarios involving rigid bodies with stacking and friction, articulated bodies connected with hard constraints, including joints with limited degrees of freedom, and stiff systems interacting with soft bodies. We present evaluations using a parallel GPU implementation that can deliver real-time performance and stable simulations with low iteration counts for millions of objects interacting via collisions, various joint/attachment constraints, and springs of various stiffness. Our results show superior performance, convergence, and stability compared to the state-of-the-art alternatives.

We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for self-intersecting objects and present a robust algorithm for computing the actual shortest boundary path. The resulting method offers an effective solution for collision and self-collision handling while simulating deformable volumetric objects, using fast simulation techniques that provide no guarantees on collision resolution. Our evaluation includes complex self-collision scenarios with a large number of active contacts, showing that our method can successfully handle them by introducing a relatively minor computational overhead.