Performance of an analogy-based all-speed procedure without any explicit damping

Abstract

The performance of a numerical method which solves¯ow at all speeds, and does not use any explicit arti®cial viscosity or damping mechanism whatsoever, is investigated by testing a number of selected cases in compressible and incompressible¯ows. Contrary to existing methods, the momentum components are chosen as the dependent variables instead of the velocity components in order to provide a number of advantages. Among the motivations for this change is a¯ow analogy which permits incompressible methods to be used to solve compressible¯ows. The method is formulated within a control-volume-based ®nite-element approach using a collocated grid arrangement. The de®nition of two types of mass¯ux components at the control volume surfaces removes the possibility of velocity-pressure decoupling in the incompressible or Euler limits. In the absence of any dissipation mechanisms, the main concern of this work is to evaluate the performance of the method and the analogy for solving high speed compressible¯ows with shocks. The results and performance of the present work are compared with the exact and benchmark solutions and the results of other workers who use dissipation mechanisms to solvē ow at all speeds.

Developing implicit pressure‐weighted upwinding scheme to calculate steady and unsteady flows on unstructured grids

“…Indeed, our experience has shown that a similar formulation has been capable of solving high-speed flow on structured quadrilateral grids. Despite using any types of limiter and/or damping functions, our results showed that the current formulation would exhibit neither undershoots and overshoots around the steep gradients nor oscillations around discontinuities [47,[52][53][54][55]. Such exhibition is normal because the derived cell-face expressions are categorized as first order.…”

Extending a Hybrid Finite-Volume-Element Method to Solve Laminar Diffusive Flame

“…This linearization is essential to treat the nonlinear momentum 188 M. DARBANDI AND M. GHAFOURIZADEH convection terms. Furthermore, Darbandi et al [21,57,58] have provided more complex linearization approaches for the nonlinear convection terms in highcompressible-flow applications. Indeed, they are not required to be elaborated here.…”

“…Darbandi and Bostandoost [5] later extended the two momentum (or velocity) components to a wide range of interpolation functions. They examined the proposed formulation in 1-D and 2-D incompressible flow cases [20,21,29]. They also studied the effectiveness and robustness of the derived expressions in suppressing unreal zigzag behavior in the flow field.…”

“…Equations (20)- (21) can be used explicitly to determine the pressure and diffusion terms appearing at any cell face.…”

“…Later, they extended their FVE method to solve fluid flow problems involving heat transfer [20]. They later evaluated the performance of their FVE method for solving high-speed compressible flows with shocks in the absence of any dissipation [21]. Darbandi and Naderi [22] extended the basic FVE method to solve flow and heat transfer on collocated hybrid grid topologies.…”