Related papers: Active flux for triangular meshes for compressible…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
We present a new way to construct analytical solutions for flow in complex microfluidic channel networks, as well as planar disordered media. Using a combination of Schwarz-Christoffel maps and segmentation techniques inspired by integrated…
Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
We consider the coupling between the equations of motion of an inviscid compressible fluid in space with an objective Cattaneo-type extension for the heat flux. These equations are written in quasilinear form and we determine which of the…
We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or…
Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large…
This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
Active Flux (AF) is a modified Finite Volume method that evolves additional Degrees of Freedom (DoF) located on the cell interfaces to compute high-order approximations to the numerical fluxes through the respective interface. We present an…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
Maxwell models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But the usual Maxwell models allow one to define well motions…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…
A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and…
In the present paper we develop the Virtual Element Method for hyperbolic problems on polygonal meshes, considering the linear wave equations as our model problem. After presenting the semi-discrete scheme, we derive the convergence…
A new Active Flux method for the multi-dimensional Euler equations is based on an additive operator splitting into acoustics and advection. The acoustic operator is solved in a locally linearized manner by using the exact evolution…
We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
Microfluidics involves the manipulation of flows at the microscale, typically requiring external power sources to generate pressure gradients. Alternatively, harnessing flows from active fluids, which are usually chaotic, has been proposed…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…