Recent work in scientific machine learning (SciML) has focused on incorporating partial
differential equation (PDE) information into the learning process. Much of this work has …

This manuscript discusses the structure of the errors in the solution of elliptic problems
introduced by the regularization of the fluid properties discontinuity in a small region of finite …

Existing work in scientific machine learning (SciML) has shown that data-driven learning of
solution operators can provide a fast approximate alternative to classical numerical partial …

A validation suite for numerical solvers calculating effective thermal conductivity in porous
media is presented. In a first step an appropriate numerical solver based on the finite volume …

Numerical discretizations of the Generalized Porous Medium Equation (GPME) with
discontinuous coefficients are analyzed with respect to the formation of numerical artifacts. In …

The role of flux-limited thermal conduction on the fusion performance of the uniaxially driven
targets studied by Derentowicz et al.[J. Tech. Phys. 18, 465 (1977) and J. Tech. Phys. 25 …

Two-dimensional three-temperature (2-D 3-T) radiation diffusion equations are widely used
to approximately describe the evolution of radiation energy within a multimaterial system …

We propose a decoupled and positivity-preserving discrete duality finite volume (DDFV)
scheme for anisotropic diffusion problems on polyhedral meshes with star-shaped cells and …

In this paper, the methods of digital rock physics are applied to determine pressure‐
dependent effective thermal conductivity in rock samples. Simulations are performed with an …

Existing work in scientific machine learning (SciML) has shown that data-driven learning of
solution operators can provide a fast approximate alternative to classical numerical partial …