Computing Fluid Flow without Grid Generation

After decades of intensive research on the shock-capturing method using Eulerian coordiantes, two drawbacks remains: (i) slip lines are poorly resolved, and (ii) prior to flow field computation, it is necessary to generate a computation grid, which can be very time consuming. Recently, a unified coordinate system was introduced by Hui et al. [1 – 4] which moves with velocity hq, q being the fluid velocity. By choosing h to preserve grid orhtongonality, it resolves slip lines sharply, get the computatioin does not break down as the Lagrangian system does. The fact that the unified coordiante system moves with velocity hq can be utilized to generate computational grid while the flow computation goes on. This is in direct contrast to the Eulerian computation, where a grid must be generated prior to flow computation, and this represents a great saving of computing time. It is noted that in typical aeronautical applications, computing the grid takes much longer time than computing the flow field itself.