Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Computational methods in Lagrangian and Eulerian hydrocodes
Computer Methods in Applied Mechanics and Engineering
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
The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
Journal of Computational Physics
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Journal of Computational Physics
A tensor artificial viscosity using a mimetic finite difference algorithm
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
We present a Lagrangian time integration scheme and compatible discretization for total energy conservation in multicomponent mixing simulations. Mixing behavior results from relative motion between species. Species velocities are determined by solving species momentum equations in a Lagrangian manner. Included in the species momentum equations are species artificial viscosity (since each species can undergo compression) and inter-species momentum exchange. Thermal energy for each species is also solved, including compression work and thermal dissipation caused by momentum exchange. The present procedure is applicable to mixing of an arbitrary number of species that may not be in pressure or temperature equilibrium. A traditional staggered stencil has been adopted to describe motion of each species. The computational mesh for the mixture is constructed in a Lagrangian manner using the mass-averaged mixture velocity. Species momentum equations are solved at the vertices of the mesh, and temporary species meshes are constructed and advanced in time using the resulting species velocities. Following the Lagrangian step, species quantities are advected (mapped) from the species meshes to the mixture mesh. Momentum exchange between species introduces work that must be included in an energy-conserving discretization scheme. This work has to be transformed to dissipation in order to effect a net change in species thermal energy. The dissipation between interacting species pairs is obtained by combining the momentum exchange work. The dissipation is then distributed to the species involved using a distribution factor based on species specific heats. The resulting compatible discretization scheme provides total energy conservation of the whole mixture. In addition, the numerical scheme includes conservative local energy exchange between species in mixture. Due to the relatively large species interaction coefficients, both the species momenta and energies are calculated implicitly. Sample calculations have yielded excellent results, including conservation of total energy in Lagrangian steps, symmetry preservation, and correct steady-state behavior.