Results 261 to 270 of about 895,705 (294)

Projection shock capturing algorithms

2008
discretized in time and space with step sizes At, £xx and Ay, t~ = n a t , xj = j£xx, Yk = kay. The numerical solution in the point (t~, xj, Yk) is denoted by uj~ and the entire solution at t ime t~ is u ~ and a function of j, k. We consider the solution of the above problem with finite difference methods.
Björn Engquist, Björn Sjögreen
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Capturing Shock Reflections: An Improved Flux Formula

Journal of Computational Physics, 1996
We consider several situations in which Roe's scheme gives incorrect results (or blows up all together), and we propose an alternative flux formula that produces numerical approximations in which the pathological behavior is either eliminated or reduced to computationally acceptable levels.
Donat, Rosa, Marquina, Antonio
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Shock capturing with Padé methods

Applied Mathematics and Computation, 1998
The article describes the development of a fourth-order Padé shock capturing method for conservation laws. Thereby, the primitive function reconstruction method proposed by \textit{C.-W. Shu} and \textit{S. Osher} [J. Comput. Phys. 77, No. 2, 439-471 (1988; Zbl 0653.65072); ibid. 83, No.
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Convergence Analysis of Shock-Capturing and Shock-Fitting Solutions on Unstructured Grids

AIAA Journal, 2014
A new shock-fitting technique for unstructured two- and three-dimensional meshes has been recently proposed and developed by the authors. In the present paper, both global and local a posteriori grid-convergence analysis is used to quantitatively measure the discretization error and order of convergence of the numerical solutions obtained using this ...
Aldo Bonfiglioli, PACIORRI, Renato
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Shock-Capturing Anomaly in the Interaction of Unsteady Disturbances with a Stationary Shock

AIAA Journal, 2021
Shock-capturing methods for numerical fluid dynamics are capable of correctly representing the flow conditions across shocks. However, there is no guarantee that the methods remain equally applicable for unsteady problems of shock–disturbance interaction. Based on the results of wide parametric computations, this paper demonstrates an inherent weakness
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Lie Symmetry Preservation and Shock-Capturing Methods

SIAM Journal on Numerical Analysis, 2008
It is known that some traditional shock-capturing schemes, including Godunov- or Roe-type schemes, generate downstream oscillatory wave patterns that cannot be effectively dampened by the dissipation methods they provide. The theme of this paper is to understand the formation and behavior at these upstream/downstream patterns from the point view of the
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A shock‐capturing scheme for body‐fitted meshes

International Journal for Numerical Methods in Fluids, 1988
AbstractA finite difference scheme based on flux difference splitting is presented for the solution of the two‐dimensional Euler equations of gas dynamics in a generalized co‐ordinate system. The scheme is based on numerical characteristic decomposition and solves locally linearized Riemann problems using upwind differencing. The decomposition is for a
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High‐order shock capturing schemes for turbulence calculations

International Journal for Numerical Methods in Fluids, 2007
AbstractThis work investigates high‐order central compact methods for simulating turbulent supersonic flows that include shock waves. Several different types of previously proposed characteristic filters, including total variation diminishing, monotone upstream‐centered scheme for conservation laws, and weighted essentially non‐oscillatory filters, are
Lo, S.-C., Blaisdell, G. A., Lyrintzis, A. S.   +2 more
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Modern shock-capturing schemes

1992
This paper discusses some of the strategies employed for shock-capturing calculations, especially of highly compressible transient flows. In most such cases, the cost of achieving given resolution can be reduced by an order of magnitude or more by employing a grid that adapts dynamically to the evolving solution.
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On Numerical Shock Instability of Low Diffusion Shock-Capturing Schemes

2019
Low diffusion shock-capturing schemes are known to produce numerical shock anomalies in hypersonic flow computations. In the current study, we conduct a stability analysis of the Roe approach. It has been found that the shock instability can be effectively suppressed if enough entropy production can be guaranteed inside the numerical shock structure ...
W. J. Xie, Ye Zhang, Ran Zhang, Hua Li
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