The spatially and temporally variable parameters and inputs to complex groundwater
models typically result in long runtimes which hinder comprehensive calibration, sensitivity …

This review attempts to summarize the physical models and advanced methods used in
computational studies of gas–liquid two-phase jet flows encountered in atomization and …

Multiscale modeling is an effective approach for investigating multiphysics systems with
largely disparate size features, where models with different resolutions or heterogeneous …

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical
time-stepping algorithms to approximate solutions. Further, many systems characterized by …

We investigate the approximate dynamics of several differential equations when the
solutions are restricted to a sparse subset of a given basis. The restriction is enforced at …

This paper reviews standard oversampling strategies as performed in the multiscale finite
element method (MsFEM). Common to those approaches is that the oversampling is …

Nonlocal models, including peridynamics, often use integral operators that embed
lengthscales in their definition. However, the integrands in these operators are difficult to …

The complex flow field in the tip region of a turbomachine rotor, including the tip leakage
flow and tip leakage vortex (TLV), has been studied for decades. Yet many associated …

A comprehensive analysis is presented for the heterogeneous multiscale method (HMM for
short) applied to various elliptic homogenization problems. These problems can be either …

Even though the art of reservoir simulation has evolved through more than four decades,
there is still a substantial research activity that aims toward faster, more robust, and more …