Tham khảo tài liệu 'applied computational fluid dynamics techniques - wiley episode 2 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 422 APPLIED COMPUTATIONAL FLUID DYNAMICS TECHNIQUES where dw x is given by the Hermitian polynomial Lohner 2001 dw 1 - 3f2 2f3 and f is defined in . The final semi-discrete scheme takes the form MiP t r ra u v P rs dw w Vd dh P where the subscripts a s and d stand for advection source and damping. This system of ODE s is integrated in time using explicit time-marching schemes . a standard five-stage Runge-Kutta scheme. . OVERALL SCHEME One complete timestep consists of the following steps - given the boundary conditions for the pressure update the solution in the 3-D fluid mesh velocities pressures turbulence variables etc. - extract the velocity vector v u v w at the free surface and transfer it to the 2-D free surface module - given the velocity field update the free surface P - transfer back the new free surface P to the 3-D fluid mesh and impose new boundary conditions for the pressure . For steady-state applications the fluid and free surface domains are updated using local timesteps. This allows some room for variants that may converge faster to the final solution . n steps of the fluid followed by m steps of the free surface complete convergence of the free surface between fluid updates etc. Empirical evidence Lohner et al. 1998 1999a c indicates that most of these variants prove unstable or do not accelerate convergence measurably. For steady-state applications it was found that an equivalent time-interval ratio between the fluid and the free surface of 1 8 yielded the fastest convergence . a Courant number of Cf for the fluid and Cs for the free surface . . MESH UPDATE Schemes that work with structured grids . Hino 1989 1997 Hino et al. 1993 Farmer et al. 1993 Martinelli and Farmer 1994 Cowles and Martinelli 1996 march the solution in time until a steady state is reached. At each timestep a volume update is followed by a free surface update. The repositioning of points at each timestep implies a complete .
