Quasi-isometric mesh movement and deformation with geometrically adaptive metric

We suggest an algorithm which allows for generation of a moving adaptive mesh with a fixed topology according to the time-dependent geometrically adaptive control metric in the computational domain using a quasi-isometric mesh quality functional. For each time step, we use the preconditioned gradient search technique for the mesh quality functional in order to compute large displacements of each mesh vertex. Intermediate meshes using simple linear interpolation between the initial and the displaced states using time as a parameter, are guaranteed to be nonsingular deformations of the initial mesh. Hence for numerical simulations with small time steps one can use single expensive variational mesh deformation algorithm per 5–10 time steps, which greatly improves the efficiency of the remeshing algorithm for moving mesh flow solvers. Control metric provides anisotropic mesh condensation near boundary of the moving body in the normal direction with special law for normal stretches in the transition zones. Algorithm for computation of target tangential stretches is crucial for realizability of control metric. It takes into account curvature of the boundary surface while small-scale features are represented via medial axis transform. Additional data are encoded on background moving mesh.