Multidimensional upwinding for incompressible flows based on characteristics

Multidimensional characteristic-based solid boundary condition for incompressible flow calculations

“…The high accuracy and fast convergence speed of MCB compared with the conventional CB scheme were reported in our previous study [20]. In the present study, we extended the concept of the multidimensional characteristics of…”

“…It is clear that the two roots of n t always have opposite signs, which indicate the pseudo-domains of dependence and the influence of the AC equations. It can be shown that the characteristic paths are given by [20]:…”

“…Traditionally, the methods used to calculate the multidimensional nature of flow in compressible flows have been designed to consider many directions for the propagation of information instead of only one direction. Previously, we introduced the first multidimensional characteristic-based scheme (MCB) for incompressible flows [20][21][22]. This scheme uses more than one direction of wave propagation by employing multidimensional characteristic paths.…”

“…This scheme uses more than one direction of wave propagation by employing multidimensional characteristic paths. For further details of this method, please refer to [20][21][22]. For the solid boundary conditions of incompressible flows, the velocity components on the solid wall are equal to the wall's velocity due to the non-penetration of mass, and thus only the pressure needs to be specified.…”

“…In all previous studies in this area, ordinary extrapolation from the interior cells in the domain near the wall has been used to estimate the pressure on solid walls. This is the case for incompressible flow simulations in conjunction with the AC method with various numerical characteristic-based schemes [10,[14][15][16][17]20], or the other schemes discussed above [5,6]. In the present study, we propose a new approach based on the multidimensional characteristic structure of AC equations near the solid walls together with the ghost cell concept for estimating pressure on the solid boundaries.…”