No abstract

SUMMARYWe apply the lattice Boltzmann (LB) method for solving the shallow water equations with source terms such as the bed slope and bed friction. Our aim is to use a simple and accurate representation of the source terms in order to simulate practical shallow water flows without relying on upwind discretization or Riemann problem solvers. We validate the algorithm on problems where analytical solutions are available. The numerical results are in good agreement with analytical solutions. Furthermore, we test the method on a practical problem by simulating mean flow in the Strait of Gibraltar. The main focus is to examine the performance of the LB method for complex geometries with irregular bathymetry. The results demonstrate its ability to capture the main flow features.

No abstract

No abstract

SUMMARYIn this paper, an optimal control problem for glass cooling processes is studied. We model glass cooling using the SP 1 approximations to the radiative heat transfer equations. The control variable is the temperature at the boundary of the domain. This results in a boundary control problem for a parabolic/elliptic system which is treated by a constrained optimization approach. We consider several cost functionals of tracking-type and formally derive the ÿrst-order optimality system. Several numerical methods based on the adjoint variables are investigated. We present results of numerical simulations illustrating the feasibility and performance of the di erent approaches.

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young-Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.

No abstract

A half space moment method to approximate the radiative heat transfer equations is investigated in one dimension. This approach leads to a hyperbolic system of equations coupled to the heat equation. Numerical results are presented together with a comparison with previous approximations.