- A Finite Difference Interpretation of the Lattice Boltzmann Method (1999)
- Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be a completely different approach to solve the incompressible Navier-Stokes equations. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side effect, new starting points for a discretization of the incompressible Navier-Stokes equations are obtained.
- A Hybrid Simulation Method for Radivative Transfer Equations (2001)
- We consider heat transfer processes where radiation in a large number of frequency bands plays a dominant role.
- A new discrete velocity method for Navier-Stokes equations (1999)
- The relation between the Lattice Boltzmann Method, which has re- cently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of Navier-Stokes equations for incom- pressible uid ow is presented by combining both the approaches. The new scheme can be interpreted as a pseudo-compressibility method and, for a particular choice of parameters, this interpretation carries over to the Lattice Boltzmann Method.
- A new perspective on kinetic schemes (1999)
- Compared to standard numerical methods for hyperbolic systems of conservation laws, Kinetic Schemes model propagation of information by particles instead of waves. In this article, the wave and the particle concept are shown to be closely related. Moreover, a general approach to the construction of Kinetic Schemes for hyperbolic conservation laws is given which summarizes several approaches discussed by other authors. The approach also demonstrates why Kinetic Schemes are particularly well suited for scalar conservation laws and why extensions to general systems are less natural.
- Consistency analysis of mesh-free methods for conservation laws (2000)
- Based on general partitions of unity and standard numerical flux functions, a class of mesh-free methods for conservation laws is derived. A Lax-Wendroff type consistency analysis is carried out for the general case of moving partition functions. The analysis leads to a set of conditions which are checked for the finite volume particle method FVPM. As a by-product, classical finite volume schemes are recovered in the approach for special choices of the partition of unity.
- Discretizations for the Incompressible Navier-Stokes Equations based on the Lattice Boltzmann Method (1999)
- A discrete velocity model with spatial and velocity discretization based on a lattice Boltzmann method is considered in the low Mach number limit. A uniform numerical scheme for this model is investigated. In the limit, the scheme reduces to a finite difference scheme for the incompressible Navier-Stokes equation which is a projection method with a second order spatial discretization on a regular grid. The discretization is analyzed and the method is compared to Chorin's original spatial discretization. Numerical results supporting the analytical statements are presented.
- Do Finite Volume Methods Need a Mesh? (2001)
- In this article, finite volume discretizations of hyperbolic conservation laws are considered, where the usual triangulation is replaced of unity on the computational domain.
- Exponentially exact hyperbolic systems (2000)
- Starting with general hyperbolic systems of conservation laws, a special sub - class is extracted in which classical solutions can be expressed in terms of a linear transport equation. A characterizing property of this sub - class which contains, for example, all linear systems and non - linear scalar equations, is the existence of so called exponentially exact entropies.