Coordinate Transformations and Numerical Grids for Solving Problems with Hybrid Layers

The paper describes an explicit approach for generating layer-damping coordinate transformations and corresponding layer-resolving grids for problems having hybrid-type layers. The grids are generated on the basis of qualitative estimates of solution derivatives in the layers of one-dimensional problems with a turning point and a small parameter in the coefficient affecting the second derivative. The paper presents results of numerical experiments, using appropriate coordinate transformations and layer-resolving grids, for two-point boundary value problems and two-dimensional Navier–Stokes equations modelling a viscous fluid flow in a cavity.