Application of the spherical metric tensor to grid adaptation and the solution of applied problems

Abstract

New results concerning the construction and application of adaptive numerical grids for solving applied problems are presented. The grid generation technique is based on the numerical solu tion of inverted Beltrami and diffusion equations for a monitor metric. The capabilities of the spherical metric tensor as applied to adaptive grid generation are examined in detail. Adaptive hexahedral grids are used to numerically solve a boundary value problem for the three dimensional heat equation with a moving boundary in a continuous medium with discontinuous thermophysical parameters; this problem models the interaction of a thermal wave with a thermocouple embedded in the solid.

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

“…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].…”

“…(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]. Inverted diffusion equations were used for adaptive mesh generation in numerical computa tions concerning nanotechnology problems [14], heat transfer in two phase media [11], and singularly perturbed diffusion problems with boundary and internal layers [13].…”

“…Numerical algorithms for adaptive grid generation based on the solution of these equations can be found in [11,13]. Inverted diffusion equations were used for adaptive mesh generation in numerical computa tions concerning nanotechnology problems [14], heat transfer in two phase media [11], and singularly perturbed diffusion problems with boundary and internal layers [13]. In an alternative approach, Eqs.…”