Surrogate modeling and uncertainty quantification tasks for PDE systems are most often
considered as supervised learning problems where input and output data pairs are used for …

The vanadium redox flow battery has been intensively examined since the 1970s, with
researchers looking at its electrochemical time varying electrolyte concentration time …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

We study the velocity boundary condition for curved boundaries in the lattice Boltzmann
equation (LBE). We propose a LBE boundary condition for moving boundaries by …

We quantitatively evaluate the capability and accuracy of the lattice Boltzmann equation
(LBE) for modeling flow through porous media. In particular, we conduct a comparative study …

This book is a revised edition of my earlier book of the same title. The cur rent edition adopts
the structure of the earlier version but is much changed. The introduction now contains …

This book presents an account of theories of? ow in porous media which have proved
tractable to analysis and computation. In particular, the t-ories of Darcy, Brinkman, and …

In many physical problems several scales present either in space or in time, caused by
either inhomogeneity of the medium or complexity of the mechanical process. A fundamental …

Coupled shear-flow tests were conducted on two artificial rock fractures with natural rock
fracture characteristics under constant normal loading boundary conditions. Numerical …

We present an overview of the mathematical issues that arise in the modeling of polymer
electrolyte membrane fuel cells. These issues range from nanoscale modeling of network …