There have been growing research interests in high-order discontinuous schemes over
recent years. With established theoretical basis and framework, more efforts have recently …

In this paper, we present fully implicit continuous Galerkin–Petrov (cGP) and discontinuous
Galerkin (dG) time‐stepping schemes for incompressible flow problems which are, in …

We present new approaches to reservoir modeling and flow simulation that dispose of the
pillar-grid concept that has persisted since reservoir simulation began. This results in …

In this paper, we develop a high-order method for the steady two-phase compressible
Navier–Stokes equations closed by generic equations of state, adapted to gas–liquid flows …

We design and analyze a Hybrid High-Order (HHO) method on unfitted meshes to
approximate elliptic interface problems by means of a consistent penalty method à la …

A modified interfacial Riemann problem accounting for phase change and surface tension
was developed to couple a reacting gas to a vaporizing compressible liquid. Results from …

We develop a stabilized cut discontinuous Galerkin framework for the numerical solution of
elliptic boundary value and interface problems on complicated domains. The domain of …

Abstract Although the Discontinuous Galerkin (dg) method has seen widespread use for
compressible flow problems in a single fluid with constant material properties, it has yet to be …

SUMMARY A discontinuous Galerkin method for the solution of the immiscible and
incompressible two‐phase flow problem based on the nonsymmetric interior penalty method …

We develop novel stabilized cut discontinuous Galerkin methods for advection-reaction
problems. The domain of interest is embedded into a structured, unfitted background mesh …