Physics-informed neural networks for highly compressible flows: assessing and enhancing shock-capturing capabilities

While physics-informed neural networks have been shown to accurately solve a wide range of fluid dynamics problems, their effectivity on highly compressible flows is so far limited. In particular, they struggle with transonic and supersonic problems that involve discontinuities such as shocks. While there have been multiple efforts to alleviate...

A study of an artificial viscosity technique for high-order discontinuous Galerkin methods

Prediction of heat loads during hypersonic re-entry is of great interest in space exploration and in the topic of space debris as well. To date, there is no accurate method to reproduce either experimentally or numerically the physics in re-entry conditions. On the numerical side, high-order discontinuous Galerkin methods have potential to...

Depth-averaged unsteady RANS simulation of resonant shallow flows in lateral cavities using augmented WENO-ADER schemes

Turbulent shallow flows are characterized by the presence of horizontal large-scale vortices, caused by local variations of the velocity field. Apart from these 2D large vortices, small scale 3D turbulence, mainly produced by the interaction of the flowing water with the solid boundaries, is also present. The energy spectrum of turbulent...

High-order shock capturing discontinuous Galerkin schemes

A shock capturing strategy for high-order accurate Discontinuous Galerkin (DG) approximations of the compressible Euler equations and the ideal magnetohydrodynamic equations is presented. Capturing of discontinuities without numerical oscillations is achieved by applying filters to the computed solution after each time step. The filter...

On the Refraction of Shock Waves at Fe-Be Interface

The paper aims to investigate the refraction phenomena of shock waves at ferrum-beryllium (Fe-Be) interface. The equations of state of Fe and Be adopt “stiffen gas” formula. For the regular refraction, the shock polar theory is employed. The critical angles of transition of the regular to irregular refraction about the different shock intensity...

Numerical schemes for the simulation of three-dimensional cardiac electrical propagation in patient-specific ventricular geometries

This paper introduces different numerical strategies in computational electrophysiology, based on the Finite Element Method to handle the space discretization of the governing equations. The long-term goal is to apply these computational techniques to study the three-dimensional electrical propagation in patient-specific ventricular geometries,...

Numerical schemes for compressible flow with all Mach numbers

This work is concerned with the numerical solution of an inviscid compressible flow. Our goal is to develop a sufficiently accurate and robust method allowing the solution of problems with a wide range of Mach numbers. The main ingredients are the discontinuous Galerkin finite element method (DGFEM), semi-implicit time stepping, special...