A non-boundary-fitted-grid method, based on compact integrated-RBF approximations, for solving differential problems in multiply-connected domains.

This paper presents a new non-boundary-fitted-grid numerical technique for solving partial differential equations (PDEs) in multi-hole domains. A multiply-connected domain is converted into a simply-connected domain of rectangular or non-rectangular shape that is discretised using a Cartesian grid. Compact radial basis function (RBF) stencils, which are constructed through integration rather than the conventional differentiation, are used to discretise the field variables. The imposition of inner boundary conditions is conducted by means of body forces that are derived from satisfying the governing equations and prescribed boundary conditions in small subregions. Salient features of the proposed method include: (i) simple pre-processing (Cartesian grid), (ii) high rates of convergence of the solution accuracy with respect to grid refinement achieved with compact integrated-RBF stencils, where both nodal function and derivative values are included in the approximations, (iii) the system matrix kept unchanged for the case of moving holes, and (iv) no interpolation between Lagrange and Euler meshes required. Several linear and nonlinear problems, including rotating-cylinder flows and buoyancy-driven flows in eccentric and concentric annuli, are simulated to verify the proposed technique. • This paper presents a new non-boundary-fitted-grid method. • The field variables are approximated using compact integrated-RBF stencils. • Body forces are derived from satisfying the PDEs and boundary conditions in subregions. • Interpolation between the two Euler and Lagrange systems is not required. • Multiply-connected domains with moving holes are considered in verification. [ABSTRACT FROM AUTHOR]