Local grid refinement

Rohde, M., Extending the Lattice-Boltzmann method—novel techniques for local grid refinement and boundary conditions , Ph.D. Thesis, Delft University of Technology, Delft, Netherlands (2004). 

For simple flows where the mean velocity and/or turbulent diffusivity depend only weakly on the spatial location, the Eulerian PDF algorithm described above will perform adequately. However, in many flows of practical interest, there will be strong spatial gradients in turbulence statistics. In order to resolve such gradients, it will be necessary to use local grid refinement. This will result in widely varying values for the cell time scales found from (7.13). The simulation time step found from (7.15) will then be much smaller than the characteristic cell time scales for many of the cells. When the simulation time step is applied in (7.16), one will find that Ni must be made unrealistically large in order to satisfy the constraint that Nf > 1 for all k. 

Standard Newton-Raphson technique for the linearly implicit treatment of the source terms. Moreover, time-step adaptation and local grid refinement procedures have been implemented, making effective use of the WENO smoothness indicators and interpolation polynomials [16], The steep temperature and mass deposition gradients in combination with the strongly non-linear subhmation kinetics require a very efficient and stable numerical implementation using higher order implicit schemes. 

The problems outlined In the previous section demand a non equidistant grid the possibility of local grid refinements Is currently being studied. 

Fig. 10.8 Illustration of the local grid refinement for allowing high-resolution simulations of the...

Fig. 10.17 (a) Illustration of the computational domain with established boundary conditions, and the local grid refinement (b), for simulating the fiow about spherical agglomerates... 

Rohde M, Derksen JJ, Van den Akker HEA An applicability study of advanced lattice-Boltzmann techniques for moving, no-slip boundaries and local grid refinement, Comput Fluids 37 1238—1252, 2008. http //dx.doi.Org/10.1016/j.compfluid.2007.10.012. 

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