Related papers: The Two-Dimensional Swept Rule Applied on Heteroge…
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities…
We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle-based fluid simulation) in three-dimensional space, we add a second simulation…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…
Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
This paper presents the numerical solution of immiscible two-phase flows in porous media, obtained by a first-order finite element method equipped with mass-lumping and flux up-winding. The unknowns are the physical phase pressure and phase…
In this paper, we describe a mathematical model and a numerical simulation method for the condenser component of a novel two-phase thermosyphon cooling system for power electronics applications. The condenser consists of a set of…
We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two…
Data flow analysis and optimization is considered for homogeneous rectangular mesh networks. We propose a flow matrix equation which allows a closed-form characterization of the nature of the minimal time solution, speedup and a simple…
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…
We introduce the radiative transfer code Sweep for the cosmological simulation suite Arepo. Sweep is a discrete ordinates method in which the radiative transfer equation is solved under the infinite speed of light, steady state assumption…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…
For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid…