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We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
We investigate hydrodynamic noise in a dilute granular gas during the homogeneous cooling state, by means of a proper application of the Direct Simulation Monte Carlo (DSMC) algorithm. The DSMC includes a source of randomization which is…
We analyze the transport properties of a low density ensemble of identical macroscopic particles immersed in an active fluid. The particles are modeled as inelastic hard spheres (granular gas). The non-homogeneous active fluid is modeled by…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
We analyze the mixed frame equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading…
Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…
The equations of relativistic hydrodynamics are transformed so that steps forward in time preserves local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to co-moving…
Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
We introduce a new algorithm for the simulation of Euclidean dynamical triangulations that mimics the Metropolis-Hastings algorithm, but where all proposed moves are accepted. This rejection-free algorithm allows for the factorization of…
We present an alternative method to estimate the numerical viscosity in simulations of astrophysical objects, which is based in the damping of fluid oscillations. We apply the method to general relativistic hydrodynamic simulations using a…
Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
We present a new mesoscale model for ionic liquids based on a low Mach number fluctuating hydrodynamics formulation for multicomponent charged species. The low Mach number approach eliminates sound waves from the fully compressible…
Fluid flow simulation is a highly active area with applications in a wide range of engineering problems and interactive systems. Meshless methods like the Moving Particle Semi-implicit (MPS) are a great alternative to deal efficiently with…
We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…
Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…