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We simulate the mesoscopic dynamics of droplets formed by phase separated fluids at nanometer scales where thermal fluctuations are significant. Both spherical droplets fully immersed in a second fluid and sessile droplets which are also in…
We introduce a lattice Boltzmann computational scheme capable of modeling thermohydrodynamic flows of monatomic gases. The parallel nature of this approach provides a numerically efficient alternative to traditional methods of computational…
We employ the principle of minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first…
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of…
Physical systems are governed by partial differential equations (PDEs). The Navier-Stokes equations describe fluid flows and are representative of nonlinear physical systems with complex spatio-temporal interactions. Fluid flows are…
We introduce a full-Lagrangian heterogeneous multiscale method (LHMM) to model complex fluids with microscopic features that can extend over large spatio-temporal scales, such as polymeric solutions and multiphasic systems. The proposed…
Over the centuries mathematicians have been challenged by the partial differential equations (PDEs) that describe the motion of fluids in many physical contexts. Important and beautiful results were obtained in the past one hundred years,…
Particle methods play an important role in the study of a wide variety of astrophysical fluid dynamics problems. The different methods currently in use are all variants of the so-called Smoothed Particle Hydrodynamics (SPH) scheme…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic particle method which allows to select the level of resolution at which a fluid is simulated. The numerical integration of its equations of motion still suffers from the lack of…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…
Understanding the physics of nonequilibrium systems remains as one of the major challenges of theoretical physics. This problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing…
This paper presents an overview and introduction to Smoothed Particle Hydrodynamics and Magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and…
One-dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
Numerical simulations have historically played a major role in understanding the hydrodynamics of the tidal disruption process. Given the complexity of the geometry of the system, the challenges posed by the problem have indeed stimulated…
Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for…
We extend recent work on hydrodynamics with global multipolar symmetries -- known as "fracton hydrodynamics" -- to systems in which the multipolar symmetries are gauged. We refer to the latter as "fracton magnetohydrodynamics", in analogy…
In this study we explore a new simulation scheme for partial differential equations known as Information Field Dynamics (IFD). Information field dynamics attempts to improve on existing simulation schemes by incorporating Bayesian field…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…