Parallel-multigrid computation of unsteady incompressible viscous flows using a matrix-free implicit method and high-resolution characteristics-based scheme

Multidimensional upwinding for incompressible flows based on characteristics

“…In this section, second-order CB scheme relations which have been used here are presented. It should be noted that these relations are based on presented CB scheme in the literature such as [8,[11][12][13][14][15]. If ðn x ; n y ; n z Þ denotes the unit normal vector to common face of two cells, the relations for determining flow quantities on the common face is as follows [11][12][13][14][15]:…”

“…The method was developed for three-dimensional flows [9] and further developed to incorporate multigrid techniques [10]. This method was extended by Zhao et al for simulation of incompressible flows and convection heat transfer on unstructured two-and three-dimensional grids [11][12][13][14][15]. Flow variables are calculated along characteristics paths in the direction normal to the surface of a control volume and their initial values are interpolated based on the signs of the corresponding characteristic speeds.…”

Multidimensional characteristic-based solid boundary condition for incompressible flow calculations

“…(17) is used for second order extrapolation to estimate the pressure on the solid wall boundary [5,6,10,15,16,18,22] because the velocity relative to the solid wall is zero due to the non-slip condition:…”

“…This method has been used widely to simulate incompressible flows in different conditions, including extensions to threedimensional flows [8] and multigrid techniques [9], porous media [10], flows with various densities [11,12], turbulent flow simulation [13], and non-Newtonian flows [14]. In addition, the CB scheme was used extensively by Zhao et al to calculate incompressible flows with energy equations to address two-and three-dimensional problems with unstructured grids in conjunction with parallel computations [15][16][17][18][19].…”

A 3D implicit unstructured-grid finite volume method for structural dynamics

“…To enhance computational efficiency, an implicit dual time-stepping scheme, which is widely used for solutions of unsteady flows in CFD [13,[15][16][17], is adopted in this work for time discretization. Implicit schemes usually permit larger time-step sizes than explicit schemes, if not taking into consideration of accuracy.…”