• Title/Summary/Keyword: 1-D Euler equations

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COMPARATIVE STUDY ON FLUX FUNCTIONS AND LIMITERS FOR THE EULER EQUATIONS (Euler 방정식의 유량함수(Flux Function)와 제한자(Limiter) 특성 비교 연구)

  • Chae, E.J.;Lee, S.
    • Journal of computational fluids engineering
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    • v.12 no.1
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    • pp.43-52
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    • 2007
  • A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's, Godunov's, Osher's(physical order and natural order), Roe's, HLLE, AUSM, AUSM+, AUSMPW+ and M-AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

SELF-SIMILAR SOLUTIONS FOR THE 2-D BURGERS SYSTEM IN INFINITE SUBSONIC CHANNELS

  • Song, Kyung-Woo
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.1
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    • pp.29-37
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    • 2010
  • We establish the existence of weak solutions in an infinite subsonic channel in the self-similar plane to the two-dimensional Burgers system. We consider a boundary value problem in a fixed domain such that a part of the domain is degenerate, and the system becomes a second order elliptic equation in the channel. The problem is motivated by the study of the weak shock reflection problem and 2-D Riemann problems. The two-dimensional Burgers system is obtained through an asymptotic reduction of the 2-D full Euler equations to study weak shock reflection by a ramp.

On the artificially-upstream flux splitting method

  • Sun M.;Takayama K.
    • 한국전산유체공학회:학술대회논문집
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    • 2003.10a
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    • pp.156-157
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    • 2003
  • A simple method is proposed to split the flux vector of the Euler equations by introducing two artificial wave speeds. The direction of wave propagation can be adjusted by these two wave speeds. This idea greatly simplifies the upwinding, and leads to a new family of upwind schemes. Numerical flux function for multi-dimensional Euler equations is formulated for any grid system, structured or unstructured. A remarkable simplicity of the scheme is that it successfully achieves one-sided approximation for all waves without recourse to any matrix operation. Moreover, its accuracy is comparable with the exact Riemann solver. For 1-D Euler equations, the scheme actually surpasses the exact solver in avoiding expansion shocks without any additional entropy fix. The scheme can exactly resolve stationary contact discontinuities, and it is also freed of the carbuncle problem in multi­dimensional computations.

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DEVELOPMENT OF A PRECONDITIONED ADJOINT METHOD FOR ALL-SPEED FLOW ANALYSES OF QUASI ONE-DIMENSIONAL EULER EQUATIONS (준 일차원 Euler 방정식의 전속도 유동해석을 위한 예조건화 수반변수 기법의 개발)

  • Lee, H.R.;Lee, S.
    • Journal of computational fluids engineering
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    • v.20 no.3
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    • pp.27-34
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    • 2015
  • In this study, preconditioned adjoint equations for the quasi one-dimensional Euler equations are developed, and their computational benefit at all speed is assessed numerically. The preconditioned adjoint equations are derived without any assumptions on the preconditioning matrix. The dissipation for Roe type numerical flux is also suggested to scale the dissipation term properly at low Mach numbers as well as at high Mach numbers. The new preconditioned method is validated against analytical solutions. The convergence characteristics over wide range of Mach numbers is evaluated. Finally, several inverse designs for the nozzle are conducted and the applicability of the method is demonstrated.

Some Modifications of MacCormark's Methods (MacCormack 방법의 개량에 대한 연구)

  • Ha, Young-Soo;Yoo, Seung-Jae
    • Convergence Security Journal
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    • v.5 no.3
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    • pp.93-97
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    • 2005
  • MacCormack's method is an explicit, second order finite difference scheme that is widely used in the solution of hyperbolic partial differential equations. Apparently, however, it has shown entropy violations under small discontinuity. This non-physical shock grows fast and eventually all the meaningful information of the solution disappears. Some modifications of MacCormack's methods follow ideas of central schemes with an advantage of second order accuracy for space and conserve the high order accuracy for time step also. Numerical results are shown to perform well for the one-dimensional Burgers' equation and Euler equations gas dynamic.

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GLOBAL EXISTENCE FOR A PARTIALLY LINEAR 3D EULER FLOW

  • Kim, Namkwon;Lkhagvasuren, Bataa
    • Journal of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.211-224
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    • 2018
  • We consider a certain three dimensional Euler flow with infinite energy, which is sometimes called the columnar or two and half dimensional flow. We prove the global smoothness of such flow in ${\mathbb{R}}^3$ when the initial data is in some Sobolev or Besov spaces and ${\partial}_3u_3$ is nonnegative.

Euler-Maruyama Numerical solution of some stochastic functional differential equations

  • Ahmed, Hamdy M.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.1
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    • pp.13-30
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    • 2007
  • In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $$du(x,\;t)\;=\;f(x,\;t,\;u_t)dt\;+\;g(x,\;t,\;u_t)dB(t),\;t\;>\;0$$ with initial data $u(x,\;0)\;=\;u_0(x)\;=\;{\xi}\;{\in}\;L^p_{F_0}\;([-{\tau},0];\;R^n)$. Here $x\;{\in}\;R^n$, ($R^n$ is the ${\nu}\;-\;dimenional$ Euclidean space), $f\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^n,\;g\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^{n{\times}m},\;u(x,\;t)\;{\in}\;R^n$ for each $t,\;u_t\;=\;u(x,\;t\;+\;{\theta})\;:\;-{\tau}\;{\leq}\;{\theta}\;{\leq}\;0\;{\in}\;C([-{\tau},\;0];\;R^n)$, and B(t) is an m-dimensional Brownian motion.

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Subsonic/Transonic Airfoil Design Using an Inverse Method (Inverse 기법을 이용한 아음속/천음속 익형 설계)

  • Lee Young-Ki;Lee Jae-Woo;Byun Yung-Hwan
    • Journal of computational fluids engineering
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    • v.3 no.1
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    • pp.46-53
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    • 1998
  • An inverse method for the subsonic and transonic airfoil design was developed using the Euler equations. Two testcases were performed. One was a verification of the method using the supercritical airfoil of the Korean mid-sized (100 passengers class) transport aircraft. The other was the design of an airfoil showing a good cruising performance (L/D ratio) in the high subsonic flow regime. These testcases demonstrated the efficiency and the robustness of the design method in the present study.

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AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

  • Odibat, Zaid M.;Momani, Shaher
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.15-27
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    • 2008
  • We present and discuss an algorithm for the numerical solution of initial value problems of the form $D_*^\alpha$y(t) = f(t, y(t)), y(0) = y0, where $D_*^\alpha$y is the derivative of y of order $\alpha$ in the sense of Caputo and 0<${\alpha}{\leq}1$. The algorithm is based on the fractional Euler's method which can be seen as a generalization of the classical Euler's method. Numerical examples are given and the results show that the present algorithm is very effective and convenient.

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