A numerical method for coupling the BGK model and Euler equations through the linearized Knudsen layer

The mathematic express of positive scheme axis-symmetric Euler equations is derived. With the numerical calculation of oblique shocks regular reflection problem, the validity of the positive scheme method and the self-programmed codes is verified. The positive scheme method is developed to solve the axis-symmetric Euler equations and then used to simulate the supersonic axis-symmetric flow over missile afterbody. The results show that: the numerical simulation match well with the experimental results and the numerical results obtained by the already existing high accuracy scheme method, the correctness of the development of positive scheme method is verified.

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Transonic Blade to Blade Calculations in an Axial, Radial or Mixed Flow Cascade Equipped With Splitter Blades

Volume 1: Aircraft Engine; Marine; Turbomachinery; Microturbines and Small Turbomachinery ◽

10.1115/85-gt-86 ◽

1985 ◽

Author(s):

Fernand Bertheau ◽

Yves Ribaud ◽

Valérie Millour

Keyword(s):

Boundary Conditions ◽

Numerical Method ◽

Euler Equations ◽

Three Dimensional ◽

Computation Time ◽

Leading Edge ◽

Computer Code ◽

Mixed Flow ◽

Three Dimensional Flow ◽

General Computer

A general computer code for pseudo-unsteady Euler equations integration in turbomachinery cascades has been developed. A quasi-three-dimensional flow hypothesis is assumed and only blade to blade calculation is considered here. Cascades may be axial, radial or mixed flow type. First the computerized quasi-orthogonal network is shown. This network takes into account splitters and is designed to reduce the computation time. Then, the numerical method is described and the major difficulties of this problem, which are boundary conditions, leading edge and trailing edge treatments, are presented. Finally, examples of calculations on turbines and compressors are given with emphasis on graphic representation.

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Impulse formulation of the Euler equations: general properties and numerical methods

Journal of Fluid Mechanics ◽

10.1017/s0022112099005170 ◽

1999 ◽

Vol 391 ◽

pp. 189-209 ◽

Cited By ~ 30

Author(s):

GIOVANNI RUSSO ◽

PETER SMEREKA

Keyword(s):

Numerical Methods ◽

Numerical Method ◽

Gauge Transformation ◽

Euler Equations ◽

Numerical Scheme ◽

Numerical Results ◽

Gauge Freedom ◽

General Properties ◽

Three Space ◽

Incompressible Euler

The gauge freedom of the incompressible Euler equations is explored. We present various forms of the Euler equations written in terms of the impulse density. It is shown that these various forms are related by a gauge transformation. We devise a numerical method to solve the impulse form of the Euler equations in a variety of gauges. The numerical scheme is implemented both in two and three space dimensions. Numerical results are presented showing that the impulse density tends to concentrate on sheets.

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A Godunov-Type Solver for the Numerical Approximation of Gravitational Flows

Communications in Computational Physics ◽

10.4208/cicp.060712.210313a ◽

2014 ◽

Vol 15 (1) ◽

pp. 46-75 ◽

Cited By ~ 2

Author(s):

J. Vides ◽

B. Braconnier ◽

E. Audit ◽

C. Berthon ◽

B. Nkonga

Keyword(s):

Numerical Method ◽

Euler Equations ◽

Numerical Experiments ◽

Numerical Approximation ◽

Source Term ◽

Poisson Model ◽

Riemann Solver ◽

Approximate Riemann Solver ◽

Relaxation Scheme ◽

Astrophysical Flows

AbstractWe present a new numerical method to approximate the solutions of an Euler-Poisson model, which is inherent to astrophysical flows where gravity plays an important role. We propose a discretization of gravity which ensures adequate coupling of the Poisson and Euler equations, paying particular attention to the gravity source term involved in the latter equations. In order to approximate this source term, its discretization is introduced into the approximate Riemann solver used for the Euler equations. A relaxation scheme is involved and its robustness is established. The method has been implemented in the software HERACLES [29] and several numerical experiments involving gravitational flows for astrophysics highlight the scheme.

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Computation of Unsteady Nozzle Flow due to Fluctuating Back-Pressure Using Euler Equations

Volume 1: Turbomachinery ◽

10.1115/94-gt-091 ◽

1994 ◽

Cited By ~ 1

Author(s):

Georg A. Gerolymos ◽

Jean-Pascal Bréus

Keyword(s):

Shock Wave ◽

Numerical Method ◽

Euler Equations ◽

Pressure Fluctuation ◽

Time Integration ◽

Inviscid Flow ◽

Back Pressure ◽

Third Order ◽

Flux Vector Splitting ◽

Fluctuation Amplitude

In this paper a numerical method is developed for the integration of the unsteady two-dimensional Euler equations using a third-order upwind-biased scheme with Van Leer flux-vector-splitting and Von Albada limiters, with MUSCL space-discretization, and an explicit two-stage Runge-Kutta time-integration procedure. The method is applied to the numerical computation of flows in a transonic nozzle with fluctuating back-pressure, and compared with available experimental data. The effects of frequency and amplitude on the shock-wave response are studied in detail. Despite the use of an inviscid flow model the unsteady pressures are quite satisfactorily predicted over the range of frequencies studied. The numerical method is then used to study the effect of the back-pressure fluctuation amplitude on the shock-wave oscillation. At large amplitudes the flowfield response to back-pressure fluctuation is essentially nonlinear.

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