Grid construction for discretely defined configurations

Application of coordinate transformations in numerical simulation of tsunami runup by the large particle method

“…A certain tradeoff making it possible to con struct a moving grid is that the shoreline is approximated by a sufficiently smooth curve tracing the evolu tion of the actual shoreline "on average." Below, we use the algorithm from [10] that generates a bound ary inconsistent grid whose cell edges may intersect the shoreline. Figure 1 shows an example of such an adaptive grid intended for the numerical solution of problem (1); the grid is finer near the shoreline.…”

“…The problem was solved using two grids: fixed in the computational domain and moving in the phys ical domain D; the latter was obtained with the help of the method described in [10,11]. As a reference curve, we used an "averaged" shoreline as described above.…”

“…A method for constructing such n dimensional transformations was described in detail in [10][11][12][13]. Below, we briefly describe it in the two dimensional case.…”

“…(6) on a uniform grid in produces a grid with mesh refinement in zones of D where Z(x) is small and with mesh coarsening in zones where Z(x) is large (see [10,11,13]). Numerical algorithms for adaptive grid generation based on the solution of these equations can be found in [11,13].…”

“…The construction of a coordinate transformation or a numerical grid must be automated to ensure operational predictions of possible effects of tsunami waves on the coastal zone. In this paper, the tsunami runup problem is solved by applying a modern technique for constructing coordinate transformations and numerical grids based on the solution of inverted Beltrami and diffusion equations (see [10]). …”