But higher the value of Re, higher will be the shape parameter. It is also found that the value of the shape parameter will be lower when the number of nodes is higher. It is found that there are optimum sets of nodes which give accurate and stable solution. The developed scheme saves 70– 80% of the CPU time for the first two model problems and at least 50% of the CPU time for NS equations than the usual RBF-FD method found in the literature. The upwind type nodes are considered to handle convective terms effectively for NS equations. Numerical studies are made by using multiquadric (MQ) RBF. The efficiency of the method is illustrated through linear convection–diffusion equation, coupled nonlinear equation and for the incompressible Navier–Stokes (NS) equations. Meshfree methods math.iit full#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. Topics for future work on the project include methods for improving the algorithm, explanations of general rules for the fractal sets, and possible applications to self-organized Nano-fractals.A method for simulating flow around the solid bodies has been presented using hybrid meshfree and mesh-based schemes. This is accompanied by a pictorial exploration of the newly sliced fractals, helping one gain insight into the previously unexplored properties of the fractals inner volumes. Once an understanding of the new method is gained, the planar slicing method is introduced along with solutions for the equations of the plane. Methods for applying and notating the new "two steps back, n steps forward” algorithm are then given. Drawing upon these concepts, a new algorithm, which combines the two-fractal construction methods, is introduced and illustrated, step-by-step. To establish concepts needed for exploring the proposed method, two-fractal construction methods (IFS and Derived) are explained in the one, two, and three-dimensional cases. Meshfree methods math.iit how to#Slicing the platonic fractal set This poster draws upon previous research on how to slice the three-dimensional fractal curve, the Menger Sponge, by introducing a new method for constructing and slicing the Platonic Fractal Set, revealing a potentially new subset of fractals.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |