Related papers: Asynchronous Discrete Event Schemes for PDEs
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We are interested in the long-time behaviour of approximate solutions to heterogeneous and anisotropic linear advection-diffusion equations in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. We…
We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order $k\ge0$ at mesh faces. The method hinges on local discrete reconstruction operators…
We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process, a vital stage in bioseparation. We prove stability and error estimates for both constant and affine…
We present a robust computational framework for advective-diffusive-reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balance property. The proposed methodology is valid on general…
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
A new numerical scheme for conservation equations based on evolution by asynchronous discrete events is presented. During each event of the scheme only two cells of the underlying Cartesian grid are active, and an event is processed as the…
We present a WENO-TVD scheme for the simulation of atmospheric phenomena. The scheme considers a spatial discretization via a second-order TVD flux based upon a flux-centered limiter approach, which makes use of high-order accurate…
The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the Discrete Fracture Network (DFN) model. A Darcy problem is solved to compute the…
We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a…
We present a novel approach that redefines the traditional interpretation of explicit and implicit discretization methods for solving a general class of advection-diffusion equations (ADEs) featuring nonlinear advection, diffusion…
In this contribution we analyze the large time behavior of a family of nonlinear finite volume schemes for anisotropic convection-diffusion equations set in a bounded bidimensional domain and endowed with either Dirichlet and / or no-flux…
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…