Related papers: Active flux for triangular meshes for compressible…
The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high…
We consider the coupling between the equations of motion of a compressible fluid in two and three space dimensions with Christov's equation for the heat flux. Christov's equation is a frame indifferent formulation of the classical model of…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
We formulate the the generalized Forchheimer equations for the three-dimensional fluid flows in rotating porous media. By implicitly solving the momentum in terms of the pressure's gradient, we derive a degenerate parabolic equation for the…
Stepwise controllable devices, such as switched capacitors or stepwise controllable loads and generators, transform the nonconvex AC optimal power flow (AC-OPF) problem into a nonconvex mixed-integer (MI) programming problem which is…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…
A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…
We propose an agent-based model of active flexible rods. Inspired by cytoskeletal flows, we introduce activity by an internal flow that contributes to the dissipative forces. The active force between our agents is central and reciprocal,…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…
In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E \textbf{92}, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it…
A conservative finite-volume framework, based on a collocated variable arrangement, for the simulation of flows at all speeds, applicable to incompressible, ideal-gas and real-gas fluids is proposed in conjunction with a fully-coupled…
Extending methods first used by Casson, we show how to verify a hyperbolic structure on a finite triangulation of a closed 3-manifold using interval arithmetic methods. A key ingredient is a new theoretical result (akin to a theorem by…
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…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
In this paper, we consider multipoint flux mixed finite element discretizations for slightly compressible Darcy flow in porous media. The methods are formulated on general meshes composed of triangles, quadrilaterals, tetrahedra or…
In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
We present a practical cell-centred volume-of-fluid method developed within a pure Eulerian setting for the simulation of compressible solid-fluid problems. The method builds on a previously published diffuse-interface Godunov-type scheme…