Applications of a comprehensive grid method to solution of three-dimensional boundary value problems

► The grid method based on Beltrami equations is applied to 3D problems. ► The grids are generated with the use of a spherical control metric. ► Singularly perturbed equations are calculated on adaptive grids. ► The adaptive grids are also used for numerical modeling of a two-phased problem. This paper describes some applications to three-dimensional problems of a comprehensive grid generation method that relies on inverted Beltrami equations in control metrics. The method enables one to generate in a unified manner both fixed and adaptive grids in domains and on surfaces with complicated geometry and/or multi-scaled physical quantities. The applications are related to the solutions of singularly perturbed equations with interior and boundary layers and to the solution of the heat equation in a two-phased medium modelling heat transfer between a solid material and an embedded thermocouple.