A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes equations can easily be applied to this fourth order compact formulation. In particular in this work the formulation is solved with an efficient numerical meth...

A fourth-order numerical method for the zero-Mach-number limit of the equations for compressible flow is presented. The method is formed by discretizing a new auxiliary variable formulation of the conservation equations, which is a variable density analog to the impulse or gauge formulation of the incompressible Euler equations. An auxiliary variable projection method is applied to this formula...

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

We present a fourth order accurate finite difference method for the elastic wave equation in second order formulation, where the fourth order accuracy holds in both space and time. The key ingredient of the method is a boundary modified fourth order accurate discretization of the second derivative with variable coefficient, (μ(x)ux)x. This discretization satisfies a summation by parts identity ...

A functionally graded material beam with generalized boundary conditions is contemplated in the present study in order to examine the deformation and stress behavior under thermal and thermo-mechanical load. Three discrete combinations of functionally graded materials have been deliberate in including a wide range of materials and material properties. The variation of material properties has be...

The recently proposed expanded mixed formulation for numerical solution of second order elliptic problems is here extended to fourth order elliptic problems. This expanded formulation for the diierential problems under consideration diiers from the classical formulation in that three variables are treated, i.e., the displacement and the stress and moment tensors. It works for the case where the...

A useful approach for long range computation of the Helmholtz equation in a waveguide is to re-formulate it as the operator diierential Riccati equation for the Dirichlet-to-Neumann (DtN) map. For waveguides with slow range dependence, the piecewise range independent approximation is used to derive a second order range stepping method for this one-way re-formulation. The range marching formulas...