http://scientiairanica.sharif.edu/article_4189_4a6700e675688a8e8f118a1b3d8702cb.pdf

Mixed discrete least squares meshless method for solving the linear and non-linear propagation problems

An Eulerian–Lagrangian mixed discrete least squares meshfree method for incompressible multiphase flow problems

A Mixed Discrete Least Squares Meshfree (MDLSM) method is proposed in this paper for the solution of incompressible Navier–Stokes equations. A semi-incremental two-step fractional projection method is first used to discretize the incompressible Navier–Stokes equations, followed by a mixed formulation used to solve the pressure equations. Using the mixed formulation, it is expected that the accuracy of the pressure approximation and in particular the pressure gradients are improved compared with that of conventional solution methods and in particular Discrete Least Squares Meshfree (DLSM) method. DLSM method is based on minimizing the least squares functional defined as the weighted summation of the squared residuals of the differential equation and its boundary conditions. The method is not subject to the Ladyzenskaja–Babuska–Brezzi (LBB) condition since it formulates the problem in the form of a minimization problem rather than a saddle-point problem. A number of numerical experiments are used to evaluate the efficiency of the proposed MDLSM method and to compare its accuracy against the DLSM method. From the results, it is found that the proposed MDLSM method can efficiently simulate the incompressible fluid flow problems. Furthermore, it can be concluded that the MDLSM method has higher accuracy compared with the DLSM method.

Mixed Discrete Least Squares Meshfree method for solving the incompressible Navier–Stokes equations

A shift‐adaptive meshfree method for solving a class of initial‐boundary value problems with moving boundaries in one‐dimensional domain

http://scientiairanica.sharif.edu/article_4203_6f92c0efb8788f8cf01aa3a39f2f8b84.pdf

Collocated Mixed Discrete Least Squares Meshless (CMDLSM) method for solving quadratic partial differential equations

An efficient adaptive node regeneration method is proposed in this paper for solving elasticity problems using the mixed discrete least squares meshless (MDLSM) method. The method starts with a point-wise error estimation of the solution produced on an arbitrary initial configuration defined by the user using the MDLSM method. The point-wise error estimate is associated with the support domain of the nodal points and used to calculate the required nodal spacing at each support domain and subsequently generate new nodes at support domain level. A node-removing process is then used to remove some of the nodes created at the overlapping regions of the support domains. To improve the quality of the final configuration, a node-moving procedure based on interpolation of the errors on the original configuration is used to create the final nodal configuration. The proposed method is a single step refinement procedure and is capable of producing nodal configurations of desired accuracy for different problems. The proposed method is used to simulate three benchmark examples from the literature and the results are produced and compared with those of the conventional multi-stage node enrichment method. The results indicate the superior efficiency and effectiveness of the proposed method compared to the available methods.

S. Nikravesh Kazeroni

Papers

An adaptive node regeneration technique for the efficient solution of elasticity problems using MDLSM method