Two-Dimensional Subsonic Flow of Compressible Fluids

Tsien, Hsue-shen

doi:10.2514/2.7045

Cited by 21 publications

(4 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…At this time, the pressure p ( ρ ) is negative, which just corresponds to the so‐called Chaplygin gas with the form

p false(ρ false) = - \frac{1}{2 ρ^{2}},

and therefore, system together with can also be called the Chaplygin Euler equations. The Chaplygin gas was introduced by Chaplygin, Tsien, and von Karman as a suitable mathematical approximation for calculating the lifting force on a wing of an airplane in aerodynamics. It is also advertised as a possible model for dark energy .…”

Section: Introductionmentioning

confidence: 99%

Interaction of delta shock waves for the Chaplygin Euler equations of compressible fluid flow with split delta functions

Zhang

Wang

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

We investigate the interaction of delta shock waves and contact discontinuities for the Chaplygin Euler equations of compressible fluid flow with split delta functions. The perturbed Riemann problem when initial data are three piecewise constant states is constructively solved, and the global structure and large time‐asymptotic behaviors of solutions are discussed case by case via deriving how the solution continues beyond points of interaction. It is shown that the Riemann solutions are stable for such small perturbations with initial data by letting perturbed parameter ε tend to zero. Moreover, some numerical simulations completely coinciding with the theoretical analysis are also exhibited.

show abstract

“…At this time, the pressure p ( ρ ) is negative, which just corresponds to the so‐called Chaplygin gas with the form

p false(ρ false) = - \frac{1}{2 ρ^{2}},

Section: Introductionmentioning

confidence: 99%

Interaction of delta shock waves for the Chaplygin Euler equations of compressible fluid flow with split delta functions

Zhang

Wang

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…The state equation is

p (ρ) MathClass-rel= MathClass-bin- \frac{1}{ρ} MathClass-punc, for ρ MathClass-rel> 0 MathClass-punc.

This model is known as the Chaplygin gas. It was introduced by Chaplygin , Tsien and von Karman as a suitable mathematical approximation for calculating the lifting force on a wing of an airplane in aerodynamics. In this model, the sound speed is given by

c MathClass-rel= \frac{1}{ρ}

and tends to zero as the density ρ tends to infinity.…”

Section: Applicationsmentioning

confidence: 99%

Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data

Shao

2013

Math Methods in App Sciences

View full text Add to dashboard Cite

“…This gas dynamics model has been advertised as a possible quintessence prototype for unifying dark matter and dark energy. When a = 1 and A = 1, Chaplygin [16] introduced it as isentropic Chaplygin gas in a particular case; Mathematically, it is employed to approximation for calculating the lifting force on an aeroplane wing in aerodynamics [17][18][19]. In solving 1 − D RP, Y. Brenier [20] found the Riemann solutions with concentration, and for the Relativistic Chaplygin gas dynamics model, Cheng and Yang [21] investigated the RP.…”

Section: Introductionmentioning

confidence: 99%

The application of differential constraint method for the solution of non-homogeneous generalized Riemann problem

Gaurav,

Singh,

Pradeep

2023

Phys. Scr.

View full text Add to dashboard Cite

This paper reports the solution to the Non-homogeneous Riemannproblem by applying the approach of differential constraint for the one-dimensional(1 − D) generalized Chaplygin gas equations with non-constant initial data. Herewe take source term as a Coulomb type constant frictional term. We reducedthe governing non-homogeneous model into a homogeneous one by introducing anew velocity variable. By virtue of this advantage of frictional type source term,we would easily determine the solution of reformulated homogeneous governingmodel. We have computed the differential constraint and its consistency condi-tions for the specified model. Moreover, we have derived here the compatibilitycondition between the governing model and the differential constraints. The solu-tions to generalized Riemann problem for the 1 − D Euler’s equation of governinggas model are obtained as well as for the smooth and non-constant initial condi-tions the comprehensive overview of the solutions is studied.

show abstract

Two-Dimensional Subsonic Flow of Compressible Fluids

Cited by 21 publications

References 32 publications

Interaction of delta shock waves for the Chaplygin Euler equations of compressible fluid flow with split delta functions

Interaction of delta shock waves for the Chaplygin Euler equations of compressible fluid flow with split delta functions

Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data

The application of differential constraint method for the solution of non-homogeneous generalized Riemann problem

Contact Info

Product

Resources

About