An exact particle method for scalar conservation laws and its application to stiff reaction kinetics

An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is as accurate as the applied ODE solver. Furthermore, the method is extended to stiff balance laws. A special correction approach yields a method that evolves detonation waves at correct velocities, without resolving their internal dynamics. The particle approach is compared to a classical finite volume method in terms of numerical accuracy, both for conservation laws and for an application in reaction kinetics.Comment: 14 page, 7 figures, presented in the Fifth International Workshop on Meshfree Methods for Partial Differential Equation

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

Numerical Methods for High and Low Speed Combustion Simulations

The numerical simulation of turbulent combustion remains one of the most challenging problems of scientific computing. Major difficulties arise from a number of specific physical properties of combustion systems, which are extremely difficult to represent by discrete numerical approximations. This article explains three key problem areas that are relevant to premixed turbulent combustion and that are related to singular limit regimes of the underlying reactive °ow equations. These problem areas are the low Mach number singularity, the deflagration and detonation discontinuity limits, and some issues arising from numerical integration of stiff and rapid chemical reaction equations. For each problem area we summarize the underlying physical processes and the relevant mathematical description, explain the associated numerical problems, and provide brief descriptions of numerical strategies to overcome them. This article is a condensation of two earlier extended reports by the author, published in Vervisch et al. (1999) and Breitung et al. (1999a)

FullSWOF: A free software package for the simulation of shallow water flows

Numerical simulations of flows are required for numerous applications, and are usually carried out using shallow water equations. We describe the FullSWOF software which is based on up-to-date finite volume methods and well-balanced schemes to solve this kind of equations. It consists of a set of open source C++ codes, freely available to the community, easy to use, and open for further development. Several features make FullSWOF particularly suitable for applications in hydrology: small water heights and wet-dry transitions are robustly handled, rainfall and infiltration are incorporated, and data from grid-based digital topographies can be used directly. A detailed mathematical description is given here, and the capabilities of FullSWOF are illustrated based on analytic solutions and datasets of real cases. The codes, available in 1D and 2D versions, have been validated on a large set of benchmark cases, which are available together with the download information and documentation at http://www.univ-orleans.fr/mapmo/soft/FullSWOF/.Comment: 38 page

Numerical simulations of fuel droplet flows using a Lagrangian triangular mesh

The incompressible, Lagrangian, triangular grid code, SPLISH, was converted for the study of flows in and around fuel droplets. This involved developing, testing and incorporating algorithms for surface tension and viscosity. The major features of the Lagrangian method and the algorithms are described. Benchmarks of the algorithms are given. Several calculations are presented for kerosene droplets in air. Finally, extensions which make the code compressible and three dimensional are discussed