The accommodative full approximation scheme–full multigrid (FAS-FMG) analogy with local refinement is adopted to achieve this efficiency. In this work, an efficient augmented local radial basis function finite difference (RBF-FD) scheme has been developed for steady convection–diffusion problems. The efficiency of any numerical scheme measures on the accuracy of the scheme and its computational time. Numerical results have been found to be in good agreement with computational and experimental results available in the literature. Flow Parameters including lift, drag, vortex shedding, and vorticity contours are calculated. Steady flow cases have been run at Reynolds numbers of 10, 20 and 40 and unsteady flow problems have been studied at Reynolds numbers of 100 and 200. Numerical tests have been performed by simulating two dimensional steady and unsteady incompressible flows around cylindrical object.

Accuracy tests of the hybrid scheme have been conducted to establish the order of accuracy. Conventional finite difference scheme has been used in the Cartesian ‘meshed’ domain.

Spatial discretization of meshfree nodes has been achieved through local radial basis functions in finite difference mode (RBF-FD). Complex geometrical shapes can therefore be dealt efficiently by using meshfree nodal cloud and computational efficiency is maintained through the use of conventional mesh-based scheme on Cartesian grid in the larger part of the domain. In the rest of the domain, conventional Cartesian grid has been used beyond the meshfree cloud. These meshfree nodes have the ability to efficiently adapt to complex geometrical shapes. In this approach, a cloud of meshfree nodes has been used in the domain around the solid body.

The presented scheme optimizes the computational efficiency by combining the advantages of both meshfree and mesh-based methods. A method for simulating flow around the solid bodies has been presented using hybrid meshfree and mesh-based schemes.

Meshfree methods math.iit