Computer Methods in Applied Mechanics and Engineering
Unsteady solution of incompressible Navier-Stokes equations
Journal of Computational Physics
Computer Methods in Applied Mechanics and Engineering
A numerical method for solving incompressible viscous flow problems
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
A unified method for computing incompressible and compressible flows in boundary-fitted coordinates
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Eigenmode analysis of boundary conditions for the one-dimensional preconditioned Euler equations
Journal of Computational Physics
High-order entropy-conservative schemes and kinetic relations for van der Waals fluids
Journal of Computational Physics
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
hpGEM---A software framework for discontinuous Galerkin finite element methods
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Hi-index | 31.45 |
Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The well-defined incompressible limit relies on using pressure primitive or entropy variables. In particular entropy variables can provide numerical methods with attractive properties, e.g. fulfillment of the second law of thermodynamics. We show how a discontinuous Galerkin finite element discretization previously used for compressible flow with an ideal gas equation of state can be extended for general fluids. We also examine which components of the numerical method have to be changed or adapted. Especially, we investigate different possibilities of solving the nonlinear algebraic system with a pseudo-time iteration. Numerical results highlight the applicability of the method for various fluids.