Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Unsteady solution of incompressible Navier-Stokes equations
Journal of Computational Physics
Computations of multi-fluid flows
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
SIAM Journal on Scientific Computing
Journal of Computational Physics
A numerical method for solving incompressible viscous flow problems
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Journal of Computational Physics
A nonlinear multigrid method for the three-dimensional incompressible Navier-Stokes equations
Journal of Computational Physics
A projection FEM for variable density incompressible flows
Journal of Computational Physics
A numerical stable method for integration of the multicomponent species diffusion equations
Journal of Computational Physics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Short note: Revision of the characteristics-based scheme for incompressible flows
Journal of Computational Physics
Short Note: On the characteristics-based ACM for incompressible flows
Journal of Computational Physics
An hybrid finite volume-finite element method for variable density incompressible flows
Journal of Computational Physics
Multidimensional upwinding for incompressible flows based on characteristics
Journal of Computational Physics
A hybrid molecular continuum method using point wise coupling
Advances in Engineering Software
Hi-index | 31.47 |
The paper presents various formulations of characteristics-based schemes in the framework of the artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. The conservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shown that in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressible flows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant density flows. The characteristics-based schemes are combined with second and third-order interpolation for increasing the computational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flows reveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergence behavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of this study.