The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics
Figure 8
Lagrangian description of fluid flow.
In the Lagrangian description of fluid flow, the cells are part of the fluid and move along with it. Consider fluid cells c1 and c2 traveling with their own local coordinate systems. The cells and their coordinate systems are both traveling rightwards at velocity u in the global coordinate system. In panel A at time t1, and in panel B at any later time t2, points xm1 and xm2 in the cells’ coordinate systems remain at the same places in those cells. No fluid crosses cell edges.