Preconditioned characteristic boundary conditions for solution of the preconditioned Euler equations at low Mach number flows

2012 ◽  
Vol 231 (12) ◽  
pp. 4384-4402 ◽  
Author(s):  
Kazem Hejranfar ◽  
Ramin Kamali-Moghadam
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Euler Equations ◽  
Low Mach Number ◽  
Characteristic Boundary

scholarly journals Exact solution and the multidimensional Godunov scheme for the acoustic equations

2022 ◽  
Author(s):  
Wasilij Barsukow ◽  
Christian Klingenberg
Keyword(s):  
Exact Solution ◽  
Mach Number ◽  
Euler Equations ◽  
Two Dimensions ◽  
Finite Volume Scheme ◽  
Godunov Scheme ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Acoustic Equations ◽  
Spatial Dimensions

The acoustic equations derived as a linearization of the Euler equations are a valuable system for studies of multi-dimensional solutions. Additionally they possess a low Mach number limit analogous to that of the Euler equations. Aiming at understanding the behaviour of the multi-dimensional Godunov scheme in this limit, first the exact solution of the corresponding Cauchy problem in three spatial dimensions is derived. The appearance of logarithmic singularities in the exact solution of the 4-quadrant Riemann Problem in two dimensions is discussed. The solution formulae are then used to obtain the multidimensional Godunov finite volume scheme in two dimensions. It is shown to be superior to the dimensionally split upwind/Roe scheme concerning its domain of stability and ability to resolve multi-dimensional Riemann problems. It is shown experimentally and theoretically that despite taking into account multi-dimensional information it is, however, not able to resolve the low Mach number limit.

scholarly journals A Hybrid Adaptive Low-Mach-Number/Compressible Method for the Euler Equations

2017 ◽  
Author(s):  
Emmanuel Motheau ◽  
Max Duarte ◽  
Ann S. Almgren ◽  
John B. Bell
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Low Mach Number

Projection method for high-order compact schemes for low Mach number flows in enclosures

2014 ◽  
Vol 24 (5) ◽  
pp. 1141-1174 ◽  
Author(s):  
Artur Tyliszczak
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Projection Method ◽  
High Order ◽  
Staggered Grid ◽  
Constant Density ◽  
Computational Domain ◽  
Content Type ◽  
Low Mach Number ◽  
Large Density

Purpose – Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low Mach number flows with large density and temperature variations. Design/methodology/approach – Low Mach number approximation approach is used in the paper combined with a predictor-corrector method and accurate compact scheme of fourth and sixth order. A novel algorithm is formulated for the projection method in which the boundary conditions for the pressure are implemented in such a way that the continuity equation is fulfilled everywhere in the computational domain, including the boundary nodes. Findings – It is shown that proposed implementation of the boundary conditions considerably improves a solution accuracy. Assessment of the accuracy was performed based on the constant density Burggraf flow and for two benchmark cases for the natural convection problems: steady flow in a square cavity and unsteady flow in a tall cavity. In all the cases the results agree very well with exemplary solutions. Originality/value – A staggered or half-staggered grid arrangement is usually used for the projection method for both constant and low Mach number flows. The staggered approach ensures stability and strong pressure-velocity coupling. In the paper a high-order compact method has been implemented in the framework of low Mach number approximation on collocated meshes. The resulting algorithm is accurate, robust for large density variations and is almost free from the pressure oscillations.

scholarly journals A hybrid adaptive low-Mach number/compressible method: Euler equations

2018 ◽  
Vol 372 ◽  
pp. 1027-1047 ◽  
Author(s):  
Emmanuel Motheau ◽  
Max Duarte ◽  
Ann Almgren ◽  
John B. Bell
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Low Mach Number

A Comparative Study of Two Preconditioners for Solving 3D Inviscid Low Speed Flows

2011 ◽  
Vol 110-116 ◽  
pp. 423-430 ◽  
Author(s):  
Kazem Hejranfar ◽  
Ramin Kamali Moghadam
Keyword(s):  
Mach Number ◽  
Comparative Study ◽  
Euler Equations ◽  
Finite Volume ◽  
Eigenvalues And Eigenvectors ◽  
Flow Solver ◽  
Low Mach Number ◽  
Euler Flow ◽  
A Cell ◽  
And Performance

In the present study, two preconditioners proposed by Eriksson, and Choi and Merkel are implemented on a 3D upwind Euler flow solver on unstructured meshes. The mathematical formulations of these preconditioning schemes for the set of primitive variables are drawn and their eigenvalues and eigenvectors are compared with each others. A cell-centered finite volume Roe's method is used for discretization of the 3D preconditioned Euler equations. The accuracy and performance of these preconditioning schemes are examined by computing low Mach number flows over the ONERA M6 wing for different conditions.

Reduced-Order Modeling of Low Mach Number Unsteady Microchannel Flows

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Leila Issa ◽  
Issam Lakkis
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Solid Boundary ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Reduced Order ◽  
Low Mach Number ◽  
First Order ◽  
Slip Boundary

We present reduced-order models of unsteady low-Mach-number ideal gas flows in two-dimensional rectangular microchannels subject to first-order slip-boundary conditions. The pressure and density are related by a polytropic process, allowing for isothermal or isentropic flow assumptions. The Navier–Stokes equations are simplified using low-Mach-number expansions of the pressure and velocity fields. Up to first order, this approximation results in a system that is subject to no-slip condition at the solid boundary. The second-order system satisfies the slip-boundary conditions. The resulting equations and the subsequent pressure-flow-rate relationships enable modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a two-dimensional channel for different values of Mach and Knudsen numbers.

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