Spectral difference method for unstructured grids I: basic formulation

An upwind finite difference scheme for meshless solvers

The current paper reports on the development and validation of a localized collocation meshless method (LCMM) to model laminar incompressible flows. A high order upwinding scheme was devised to dampen the numerical oscillations arising in convection-dominated flows. Subsequently, the LCMM was analytically validated and demonstrated to yield third-order accurate solutions when compared to a benchmark analytical decaying vortex solution. Numerical validations are provided by comparison with the finite volume commercial (FVM) solver Fluent 6.2. The flow geometry for the numerical validation arises from a biomedical application that consists of modeling blood flow in the interconnection between a bypass graft and an artery. Very good agreement was found between the LCMM and the FVM.

A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics

A simple but versatile numerical technique using generalized finite difference discretization has been developed for heat transfer problems involving high convective heat flow, irregular geometry and high local thermal gradients. Upwind differencing is utilized to stabilize the numerical oscillations often induced in convection-dominated heat transfer problems. An arbitrary irregular mesh scheme is adopted to treat the irregular geometry and to achieve high accuracy in zones having high thermal gradients. To demonstrate the validity of the formulation procedure, results predicted from the present scheme are compared with the analytical solution for a problem having a regular boundary. Application to a typical metal-forming process having curved boundaries is then included.

A generalized finite difference scheme for convection-dominated metal-forming problems

Turbulent flow computations on a hybrid cartesian point distribution using meshless solver LSFD-U

A simple and efficient finite-difference technique using the generalized finite-difference (GFD) discretization is presented for two-dimensional heat transfer problems of irregular geometry. A finite number of nodal points are distributed in the problem domain. At every interior node the spatial derivatives of a field equation are approximated by functional values at neighboring nodes after introducing a family of shape functions for the dependent variables. The resulting simultaneous algebraic equations are solved in a usual manner. The results of two examples, a steady-state heat conduction and a steady natural convection problem, are compared with results of the finite-element and conventional finite-difference method, respectively. The present study demonstrates that, if well implemented, this method will become a handy yet efficient tool for solutions to any field problems since its mathematical concept is simple and the problem formulation is straightforward.

A generalized finite-difference method for heat transfer problems of irregular geometries

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A generalized finite-difference method for heat transfer problems of irregular geometries