Work

Discontinuous in Time Virtual Element Method for Darcy Equations Coupled with Multi Species Transport with First Order Reaction Network

Year: 2026

Type: article

Abstract: We study transport phenomena involving chemically reactive species, modeled by advection–diffusion–reaction systems coupled with flow fields governed by Darcy’s law. Both the velocity field and the species concentrations are discretized using the Virtual Element Method, while time integration is performed through a discontinuous Galerkin scheme. This work represents a preliminary study, in which we introduce some simplifications of the full model. In particular, we assume a concentration-independent viscosity in the Darcy problem, constant diffusion tensors in the advection–-diffusion-–reaction systems, and first-order reaction networks with liquid-phase degradation. We derive an abstract error estimate by means of a technique that combines Gauss–Radau interpolation with numerical integration. The theoretical results are supported by numerical experiments that exhibit arbitrary-order accuracy in both space and time.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-026-03428-z

Authors: Ruben Caraballo, Franco Dassi

Institution: University of Milano-Bicocca

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290