An upwind second-order scheme for compressible duct flows
SIAM Journal on Scientific and Statistical Computing
Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux
Journal of Computational Physics
Vorticity errors in multidimensional Lagrangian codes
Journal of Computational Physics
Algebraic limitations on two-dimensional hydrodynamics simulations
Journal of Computational Physics
Numerical preservation of symmetry properties of continuum problems
Journal of Computational Physics
Journal of Computational Physics
Formulations of artificial viscosity for multi-dimensional shock wave computations
Journal of Computational Physics
The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
Journal of Computational Physics
Journal of Computational Physics
A tensor artificial viscosity using a mimetic finite difference algorithm
Journal of Computational Physics
A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods
Journal of Computational Physics
Remark on the generalized Riemann problem method for compressible fluid flows
Journal of Computational Physics
A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems
SIAM Journal on Scientific Computing
Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method
Journal of Computational Physics
Journal of Computational Physics
An approach for treating contact surfaces in Lagrangian cell-centered hydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
The goal of this paper is to present high-order cell-centered schemes for solving the equations of Lagrangian gas dynamics written in cylindrical geometry. A node-based discretization of the numerical fluxes is obtained through the computation of the time rate of change of the cell volume. It allows to derive finite volume numerical schemes that are compatible with the geometric conservation law (GCL). Two discretizations of the momentum equations are proposed depending on the form of the discrete gradient operator. The first one corresponds to the control volume scheme while the second one corresponds to the so-called area-weighted scheme. Both formulations share the same discretization for the total energy equation. In both schemes, fluxes are computed using the same nodal solver which can be viewed as a two-dimensional extension of an approximate Riemann solver. The control volume scheme is conservative for momentum, total energy and satisfies a local entropy inequality in its first-order semi-discrete form. However, it does not preserve spherical symmetry. On the other hand, the area-weighted scheme is conservative for total energy and preserves spherical symmetry for one-dimensional spherical flow on equi-angular polar grid. The two-dimensional high-order extensions of these two schemes are constructed employing the generalized Riemann problem (GRP) in the acoustic approximation. Many numerical tests are presented in order to assess these new schemes. The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of our new schemes.