Simulating the interactions between fluids and porous media has attracted significant attention in computer graphics. A key challenge in this domain is modeling the Poro-Elasto-Capillary (PEC) coupling effect which describes the intricate interplay of three physical phenomena in soft porous materials: pore-structure evolution, elastic deformation, and wetting driven by capillary pressure. These phenomena collectively govern dynamic behavior such as the softening and fracturing of biscuits upon water absorption or the swelling of cellulose sponges due to liquid infiltration. Most existing simulation methods model porous media either as static grids or as solid particles with augmented water content attributes, failing to capture the full spectrum of PEC-driven effects due to the lack of physical modeling for elasticity, dynamic porosity changes, and capillary interactions. We propose a multiphase particle-based framework to holistically simulate PEC coupling effects with porous media. We develop a physics-driven model that captures elasticity and dynamic pore-structure evolution under capillary action, enabling realistic simulation of softening and swelling. We derive a saturation-aware pressure Poisson equation to enforce fluid incompressibility within and around the porous medium, ensuring accurate capillary-driven flow while preserving mass and momentum. Finally, we propose a representative elementary volume-based formulation to unify the modeling of homogeneous macro-porous media and cavity-embedded structures, enhancing the representation of pore-scale PEC effects. Comparisons with prior work and real footage show the advantages of our approach in achieving visually realistic fluid-porous media interactions.

ABSTRACT We propose a novel simulation method for surface tension effects based on the Smoothed Particle Hydrodynamics framework, capturing versatile tension effects using a unified interface energy description. Guided by the principle of energy minimization, we compute the interface energy from multiple interfaces solely using the original kernel function estimation, which eliminates the dependence on second‐order derivative discretization. Subsequently, we incorporate an inertia term into the energy function to strike a balance between tension effects and other forces. To simulate tension, we propose an energy diffusion‐based method for minimizing the objective energy function. The particles at the interface are iteratively shifted from high‐energy regions to low‐energy regions through several iterations, thereby achieving global interface energy minimization. Furthermore, our approach incorporates surface tension parameters as variable quantities within the energy framework, enabling automatic resolution of tension spatial gradients without requiring explicit computation of interfacial gradients. Experimental results demonstrate that our method effectively captures the wetting, capillary, and Marangoni effects, showcasing significant improvements in both the accuracy and stability of tension simulation.

We present a Lagrangian dynamic importance Monte Carlo method without non-trivial random walks for solving the Velocity-Vorticity Poisson Equation (VVPE) in Smoothed Particle Hydrodynamics (SPH) for vortical flows. Key to our approach is the use of the Kinematic Vorticity Number (KVN) to detect vortex cores and to compute the KVN-based importance of each particle when solving the VVPE. We use Adaptive Kernel Density Estimation (AKDE) to extract a probability density distribution from the KVN for the the Monte Carlo calculations. Even though the distribution of the KVN can be non-trivial, AKDE yields a smooth and normalized result which we dynamically update at each time step. As we sample actual particles directly, the Lagrangian attributes of particle samples ensure that the continuously evolved KVN-based importance, modeled by the probability density distribution extracted from the KVN by AKDE, can be closely followed. Our approach enables effective vortical flow simulations with significantly reduced computational overhead and comparable quality to the classic Biot-Savart law that in contrast requires expensive global particle querying.

The real-time generation of editable mesh animations in XR applications has been a focal point of research in the XR field. However, easily controlling the generated editable meshes remains a significant challenge. Existing methods often suffer from slow generation speeds and suboptimal results, failing to accurately simulate target objects' complex details and shapes, which does not meet user expectations. Additionally, the final generated meshes typically require manual user adjustments, and it is difficult to generate multiple target models simultaneously. To overcome these limitations, a universal control scheme for particles based on the sampling features of the target is proposed. It introduces a spatially adaptive control algorithm for particle coupling by adjusting the magnitude of control forces based on the spatial features of model sampling, thereby eliminating the need for parameter dependency and enabling the control of multiple types of models within the same scene. We further introduce boundary correction techniques to improve the precision in generating target shapes while reducing particle splashing. Moreover, a distance-adaptive particle fragmentation mechanism prevents unnecessary particle accumulation. Experimental results demonstrate that the method has better performance in controlling complex structures and generating multiple targets at the same time compared to existing methods. It enhances control accuracy for complex structures and targets under the condition of sparse model sampling. It also consistently delivers outstanding results while maintaining high stability and efficiency. Ultimately, we were able to create a set of smooth editable meshes and developed a solution for integrating this algorithm into VR and AR animation applications.

Abstract For vortex particle methods relying on SPH‐based simulations, the direct approach of iterating all fluid particles to capture velocity from vorticity can lead to a significant computational overhead during the Biot‐Savart summation process. To address this challenge, we present a Monte Carlo vortical smoothed particle hydrodynamics (MCVSPH) method for efficiently simulating turbulent flows within an SPH framework. Our approach harnesses a Monte Carlo estimator and operates exclusively within a pre‐sampled particle subset, thus eliminating the need for costly global iterations over all fluid particles. Our algorithm is decoupled from various projection loops which enforce incompressibility, independently handles the recovery of turbulent details, and seamlessly integrates with state‐of‐the‐art SPH‐based incompressibility solvers. Our approach rectifies the velocity of all fluid particles based on vorticity loss to respect the evolution of vorticity, effectively enforcing vortex motions. We demonstrate, by several experiments, that our MCVSPH method effectively preserves vorticity and creates visually prominent vortical motions.

Abstract We propose an SPH‐based method for simulating viscoelastic non‐Newtonian fluids within a multiphase framework. For this, we use mixture models to handle component transport and conformation tensor methods to handle the fluid's viscoelastic stresses. In addition, we consider a bonding effects network to handle the impact of microscopic chemical bonds on phase transport. Our method supports the simulation of both steady‐state viscoelastic fluids and discontinuous shear behavior. Compared to previous work on single‐phase viscous non‐Newtonian fluids, our method can capture more complex behavior, including material mixing processes that generate non‐Newtonian fluids. We adopt a uniform set of variables to describe shear thinning, shear thickening, and ordinary Newtonian fluids while automatically calculating local rheology in inhomogeneous solutions. In addition, our method can simulate large viscosity ranges under explicit integration schemes, which typically requires implicit viscosity solvers under earlier single‐phase frameworks.

Physics-based fluid simulation has played an increasingly important role in the computer graphics community. Recent methods in this area have greatly improved the generation of complex visual effects and its computational efficiency. Novel techniques have emerged to deal with complex boundaries, multiphase fluids, gas–liquid interfaces, and fine details. The parallel use of machine learning, image processing, and fluid control technologies has brought many interesting and novel research perspectives. In this survey, we provide an introduction to theoretical concepts underpinning physics-based fluid simulation and their practical implementation, with the aim for it to serve as a guide for both newcomers and seasoned researchers to explore the field of physics-based fluid simulation, with a focus on developments in the last decade. Driven by the distribution of recent publications in the field, we structure our survey to cover physical background; discretization approaches; computational methods that address scalability; fluid interactions with other materials and interfaces; and methods for expressive aspects of surface detail and control. From a practical perspective, we give an overview of existing implementations available for the above methods.

Abstract This paper introduces a particle‐based framework for simulating the behavior of elastoplastic materials and the formation of fractures, grounded in Peridynamic theory. Traditional approaches, such as the Finite Element Method (FEM) and Smoothed Particle Hydrodynamics (SPH), to modeling elastic materials have primarily relied on discretization techniques and continuous constitutive model. However, accurately capturing fracture and crack development in elastoplastic materials poses significant challenges for these conventional models. Our approach integrates a Peridynamic‐based elastic model with a density constraint, enhancing stability and realism. We adopt the Von Mises yield criterion and a bond stretch criterion to simulate plastic deformation and fracture formation, respectively. The proposed method stabilizes the elastic model through a density‐based position constraint, while plasticity is modeled using the Von Mises yield criterion within the bond of particle paris. Fracturing and the generation of fine fragments are facilitated by the fracture criterion and the application of complementarity operations to the inter‐particle connections. Our experimental results demonstrate the efficacy of our framework in realistically depicting a wide range of material behaviors, including elasticity, plasticity, and fracturing, across various scenarios.

Particle-based simulations have become increasingly popular in real-time applications due to their efficiency and adaptability, especially for generating highly dynamic fluid effects. However, the swift and stable simulation of interactions among distinct fluids continues to pose challenges for current mixture model techniques. When using a single-mixture flow field to represent all fluid phases, numerical discontinuities in phase fields can result in significant losses of dynamic effects and unstable conservation of mass and momentum. To tackle these issues, we present an advanced implicit mixture model for smoothed particle hydrodynamics. Instead of relying on an explicit mixture field for all dynamic computations and phase transfers between particles, our approach calculates phase momentum sources from the mixture model to derive explicit and continuous velocity phase fields. We then implicitly obtain the mixture field using a phase-mixture momentum-mapping mechanism that ensures conservation of incompressibility, mass, and momentum. In addition, we propose a mixture viscosity model and establish viscous effects between the mixture and individual fluid phases to avoid instability under extreme inertia conditions. Through a series of experiments, we show that, compared to existing mixture models, our method effectively improves dynamic effects while reducing critical instability factors. This makes our approach especially well-suited for long-duration, efficiency-oriented virtual reality scenarios.

We present a particle-based smoothed particle hydrodynamics (SPH) framework for simulating hyperelastic materials with anisotropic stiffness models . While most elastic simulations predominantly rely on mesh-based approaches, such as the Finite Element method , the relationship between Lamé’s first parameter and Poisson’s ratio complicates the strict enforcement of volume conservation, making it challenging to stabilize simulations for common biological tissues like fat and muscle. In this paper, we couple an implicit divergence-free SPH solver with particle-based deformation gradient computation and apply various elastic energy functions to achieve incompressible elastic simulations. The incompressibility of elastic objects and collisions between different bodies are managed by the implicit SPH algorithm. We further incorporate anisotropic energy functions, constructed from the extrapolation of Cauchy–Green invariants, to introduce anisotropic properties to the objects. By integrating activation and contraction coefficients into the energy functions, particles can simulate muscle contractions and lift heavy objects. Our method can effectively represent elastic objects with varying mechanical properties across different directions and be further employed to mimic muscle contractions. Experiments demonstrate that our approach provides realistic simulations for a wide range of animal and human body movements.

This paper proposes a real-time fluid rendering method based on the screen space rendering scheme for particle-based fluid simulation. Our method applies anisotropic transformations to the point sprites to stretch the point sprites along appropriate axes, obtaining smooth fluid surfaces based on the weighted principal components analysis of the particle distribution. Then we combine the processed anisotropic point sprite information with popular screen space filters like curvature flow and narrow-range filters to process the depth information. Experiments show that the proposed method can efficiently resolve the issues of jagged edges and unevenness on the surface that existed in previous methods while preserving sharp high-frequency details.

Abstract Fluid simulation has been one of the most critical topics in computer graphics for its capacity to produce visually realistic effects. The intricacy of fluid simulation manifests most with interacting dynamic elements. The coupling for such scenarios has always been challenging to manage due to the numerical instability arising from the coupling boundary between different elements. Therefore, we propose an implicit smoothed particle hydrodynamics fluid‐elastic coupling approach to reduce the instability issue for fluid‐fluid, fluid‐elastic, and elastic‐elastic coupling circumstances. By deriving the relationship between the universal pressure field with the incompressible attribute of the fluid, we apply the number density scheme to solve the pressure Poisson equation for both fluid and elastic material to avoid the density error for multi‐material coupling and conserve the non‐penetration condition for elastic objects interacting with fluid particles. Experiments show that our method can effectively handle the multiphase fluids simulation with elastic objects under various physical properties.

Abstract Fluid simulation is well‐known for being visually stunning while computationally expensive. Spatial adaptivity can effectively ease the computational cost by discretizing the simulation space with varying resolutions. Adaptive methods nowadays mainly focus on the mechanism of refining the fluid surfaces to obtain more vivid splashes and wave effects. But such techniques hinder further performance gain under the condition where most of the vast fluid surface is tranquil. Moreover, energetic flow beneath the surface cannot be adequately captured with the interior of the fluid still being simulated under coarse discretization. This article proposes a novel boundary‐distance based adaptive method for smoothed particle hydrodynamics fluid simulation. The signed‐distance field constructed with respect to the coupling boundary is introduced to determine particle resolution in different spatial positions. The resolution is maximal within a specific distance to the boundary and decreases smoothly as the distance increases until a threshold is reached. The sizes of the particles are then adjusted towards the resolution via splitting and merging. Additionally, a wake flow preservation mechanism is introduced to keep the particle resolution at a high level for a period of time after a particle flows through the boundary object to prevent the loss of flow details. Experiments show that our method can refine fluid–solid coupling details more efficiently and effectively capture dynamic effects beneath the surface.

Vitrectomy combined with silicone oil tamponade is an effective treatment for rhegmatogenous retinal detachment (RRD). The high viscosity and surface tension of the silicone oil make it suitable for treating large retinal tears by pressing against the retina. However, silicone oil becomes emulsified over time as it remains in the eye, which can cause serious complications. Clear visual acquisitions of silicone oil-water interaction and silicone oil emulsification progress are difficult during and after the surgery. To help doctors and patients perceive the two-phase interaction and emulsification progress intuitively, we propose a physically based simulation method for intraocular silicone oil visualization. For the visualization of immiscible silicone oil-water interaction, we introduce a volume-incompressible Smoothed Particle Hydrodynamics (SPH) approach to improve simulation precision of multiphase flow coupling. A diffusion model based on volume fraction is proposed to visualize emulsification progress. Additionally, we combine our method with cohesion and surface-minimization driven surface tension model to describe the high surface tension of silicone oil. Experiments show that our scheme can obtain a precise pressure gradient near phase boundary and perform noticeable mixing effect that evolves over time. Our method has the advantage of higher accuracy than other visualization methods, and has the potential to help doctors make decisions and estimate surgical outcomes.

Abstract A major issue in smoothed particle hydrodynamics (SPH) approaches is the numerical dissipation during the projection process, especially under coarse discretizations. High‐frequency details, such as turbulence and vortices, are smoothed out, leading to unrealistic results. To address this issue, we introduce a vorticity refinement (VR) solver for SPH fluids with negligible computational overhead. In this method, the numerical dissipation of the vorticity field is recovered by the difference between the theoretical and the actual vorticity, so as to enhance turbulence details. Instead of solving the Biot‐Savart integrals, a stream function, which is easier and more efficient to solve, is used to relate the vorticity field to the velocity field. We obtain turbulence effects of different intensity levels by changing an adjustable parameter. Since the vorticity field is enhanced according to the curl field, our method can not only amplify existing vortices, but also capture additional turbulence. Our VR solver is straightforward to implement and can be easily integrated into existing SPH methods.

A critical problem of Smooth Particle Hydrodynamics (SPH) methods is the numerical dissipation in viscosity computation. This leads to unrealistic results where high frequency details, like turbulence, are smoothed out. To address this issue, we introduce a viscosity-based vorticity correction scheme for SPH fluids, without complex time integration or limited time steps. In our method, the energy difference in viscosity computation is used to correct the vorticity field. Instead of solving Biot-Savart integrals, we adopt stream function, which is easier to solve and more efficient, to recover the velocity field from the vorticity difference. Our method can increase the existing vortex significantly and generate additional turbulence at potential position. Moreover, it is simple to implement and can be easily integrated with other SPH methods.