We develop error-control based time integration algorithms for compressible fluid dynamics
(CFD) applications and show that they are efficient and robust in both the accuracy-limited …

This work reports on the performances of a fully-discrete hp-adaptive entropy stable
discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations …

In computational fluid dynamics, the demand for increasingly multidisciplinary reliable
simulations, for both analysis and design optimization purposes, requires transformational …

Recently, relaxation methods have been developed to guarantee the preservation of a
single global functional of the solution of an ordinary differential equation. Here, we …

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a
semi-discrete entropy inequality under appropriate boundary conditions. In this work, we …

Provably stable flux reconstruction (FR) schemes are derived for partial differential
equations cast in curvilinear coordinates. Specifically, energy stable flux reconstruction …

Industrially relevant computational fluid dynamics simulations frequently require vast
computational resources that are only available to governments, wealthy corporations, and …

To achieve genuine predictive capability, an algorithm must consistently deliver accurate
results over prolonged temporal integration periods, avoiding the unwarranted growth of …

We develop a novel entropy–stable discontinuous Galerkin approximation of the
incompressible Navier–Stokes/Cahn–Hilliard system for p–non–conforming elements. This …

Reaction-diffusion equations model various biological, physical, sociological, and
environmental phenomena. Often, numerical simulations are used to understand and …