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

• Published in: Computational mathematics and mathematical physics Vol. 52; no. 4; pp. 548 - 564
• Main Authors: Kofanov, A. V., Liseikin, V. D., Rychkov, A. D.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.04.2012; Springer Nature B.V
• Subjects: Adaptation; Applied mathematics; Boundaries; Boundary value problems; Computational mathematics; Computational Mathematics and Numerical Analysis; Finite element method; Grid generation; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Numerical analysis; Physics; Studies; Tensors; Thermophysical; adaptive grid generation; spherical monitor metric; three-dimensional heat equation; numerical solution of applied problems
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542512040094

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 solution 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.