We present a two-level finite element method (TLFEM) with triangle element enriched with residual-free bubble (RFB) functions for the Stokes equations. For approximating solutions of RFB in each triangle element, we propose an auxiliary problem with a corrector to stabilize the pressure field. Finally we discuss the numerical stability of RFB for diffusion dominated flows in the mixed variational problem through some numerical experiments.
We have studied the effect of mountain wave on the transport of Yellow Sand by 2-dimensional simulation. The advection-diffusion equation of scalar concentration is solved to simulate the transport of Yellow Sand. Two different models are employed, one is a one-layer model in which the density gradient is constant in the entire domain, and the other is a two-layer model in which the density gradient changes at 11 km altitude. In the both models the air parcel at a high altitude starts descending toward the ground behind the mountain as the atmospheric stability increases. In the two-layer model, trapped mountain waves become strong and rotors are also generated. The scalar concentration diffuses strongly in wave breaking and rotor regions. The ground scalar concentrations of the two-layer model are very large, compared with those by the one-layer model.
In this study, acoustic propagation is computed based on lattice Boltzmann method (LBM). Linearized form of lattice Boltzmann equation (LBE) is used as a governing equation in order to capture the small acoustic perturbation. Additionally, implementations of farfield boundary condition and a monopole sound source are described in detail. The current code has a potential to solve acoustic propagation from non-compact body, including non-uniform mean flow effect and reflection at the wall. Several benchmark problems are solved, and current results show good agreement with the analytical results.
A series of spectral models which facilitate the execution of standard numerical experiments in geophysical fluid dynamics problems have been developed. Readability and modifiability of the program source codes are given priority in its design. The introduction of systematic function naming rules and the utilization of array-handling features enhanced by Fortran90 have permitted the program source codes to be written in a form that may be readily derived from the mathematical expressions of the original governing equations.
Chapt.3 describes simultaneous measurement techniques of particle size and velocity with LDA system which contribute to the analysis on two-phase turbulence modification.