https://hal.inria.fr/inria-00073529/document

On the behaviour of upwind schemes in the low Mach number limit

▪ Abstract An overview of preconditioning for the steady-state compressible inviscid fluid dynamic equations is presented. Extensions to the Navier-Stokes equations are also considered. These preconditioners are necessary for many algorithms in order to have the correct behavior at low speeds and to converge to the solution of the incompressible equations as the Mach number goes to zero. In addition, the preconditioning accelerates the convergence to a steady state for problems in which a significant portion of the flow is low speed. This low speed preconditioner can be combined with Jacobi and line preconditioners to damp high frequencies at all speeds. This is necessary for use with multigrid methods. Such combined methods are also better at accelerating problems with high aspect ratios. Details of the implementation are presented including several different variants for the preconditioning matrix.

Preconditioning techniques in computational fluid dynamics

Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon

https://www-sop.inria.fr/members/Herve.Guillard/Mywebpage/MESPUBLIS/A2004/A2004Guillard_Murrone_CF.pdf

On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes

In this work, a compressible Reynolds-averaged Navier-Stokes solver is used to investigate the aerodynamics of a microscale coaxial-rotor configuration in hover, to evaluate the predictive capability of the computational approach and to characterize the unsteadiness in the aerodynamic flowfield of the microscale coaxial systems. The overall performance is well-predicted for a range of rpm and rotor spacing. As the rotor spacing increases, the top-rotor thrust increases and the bottom-rotor thrust decreases, while the total thrust remains fairly constant. The thrusts approach a constant value at very large rotor spacing. Top rotor contributes about 55 % of the total thrust at smaller rotor spacing, which increases to about 58% at the largest rotor separation. The interaction between the rotor systems is seen to generate significant impulses in the instantaneous thrust and power. Unsteadiness is mainly caused due to blade loading and wake effect. Additional high-frequency unsteadiness was also seen due to shedding near the trailing edge. The phasing of the top vortex impingement upon the bottom rotor plays a significant role in the amount of unsteadiness for the bottom rotor. Interaction of the top-rotor tip vortex and inboard sheet with the bottom rotor results in a highly three-dimensional shedding on the upper surface of the blade in the outboard region and a two-dimensional shedding on the lower surface at the inboard portion of the blade. The wake of the top rotor contracts faster compared with that of the bottom rotor because of the vortex-vortex interaction. Further, the top-rotor wake convects vertically down at a faster rate due to increased inflow.

/pdf/computational-investigation-of-micro-scale-coaxial-rotor-2zu6sjh2te.pdf

Computational investigation of micro-scale coaxial rotor aerodynamics in hover

Assessment of Preconditioning Methods for Multidimensional Aerodynamics

Accurate flux vector splitting for shocks and shear layers

The present report investigates the use of the unsteady compressible flow problems. For low speed flow the system is stiff since the ratio of the convective speed of sound is very small. To overcome this difficulty we alter the time dependency of the equations while retaining the same steady state operator. In order to achieve high numerical resolution we also alter the artificial dissipation of the numerical scheme. The definition of preconditioners and artificial dissipation terms can be formulated conveniently by using other sets of dependent variables rather than the conservative variables. The effects of different preconditioners, artificial dissipation and grid density on accuracy and convergence to the steady state of the numerical solutions are presented in detail. The numerical results obtained for inviscid and viscous 2D and 3D flows indicate that efficient multigrid computations of flows with very low Mach numbers are now.

Norbert Kroll

Papers

Assessment of Preconditioning Methods for Multidimensional Aerodynamics

Accurate flux vector splitting for shocks and shear layers

Assessment of Preconditioning Methods

Advances in Simulation of Wing and Nacelle Stall