A Stability Analysis of Hybrid Schemes to Cure Shock Instability

2014 ◽  
Vol 15 (5) ◽  
pp. 1320-1342 ◽  
Author(s):  
Zhijun Shen ◽  
Wei Yan ◽  
Guangwei Yuan
Keyword(s):  
Stability Analysis ◽  
High Resolution ◽  
Euler Equations ◽  
Hybrid Method ◽  
Numerical Experiments ◽  
Physical Phenomenon ◽  
Numerical Instability ◽  
Hybrid Schemes ◽  
Carbuncle Phenomenon ◽  
Spurious Solution

AbstractThe carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving methods. The hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical phenomenon. In this paper, a matrix-based stability analysis for 2-D Euler equations is performed to explore the cause of instability of numerical schemes. By combining theRoewithHLLflux in different directions and different flux components, we give an interesting explanation to the linear numerical instability. Based on such analysis, some hybrid schemes are compared to illustrate different mechanisms in controlling shock instability. Numerical experiments are presented to verify our analysis results. The conclusion is that the scheme of restricting directly instability source is more stable than other hybrid schemes.

Axisymmetric Hurricane in a Dry Atmosphere: Theoretical Framework and Numerical Experiments

2011 ◽  
Vol 68 (8) ◽  
pp. 1607-1619 ◽  
Author(s):  
Agnieszka A. Mrowiec ◽  
Stephen T. Garner ◽  
Olivier M. Pauluis
Keyword(s):  
Water Vapor ◽  
High Resolution ◽  
Numerical Model ◽  
Numerical Experiments ◽  
Momentum Flux ◽  
Theoretical Framework ◽  
Moist Processes ◽  
Energy And Momentum ◽  
The Relationship ◽  
Theoretical Insight

Abstract This paper discusses the possible existence of hurricanes in an atmosphere without water vapor and analyzes the dynamic and thermodynamic structures of simulated hurricane-like storms in moist and dry environments. It is first shown that the “potential intensity” theory for axisymmetric hurricanes is directly applicable to the maintenance of a balanced vortex sustained by a combination of surface energy and momentum flux, even in the absence of water vapor. This theoretical insight is confirmed by simulations with a high-resolution numerical model. The same model is then used to compare dry and moist hurricanes. While it is found that both types of storms exhibit many similarities and fit well within the theoretical framework, there are several differences, most notably in the storm inflow and in the relationship between hurricane size and intensity. Such differences indicate that while water vapor is not necessary for the maintenance of hurricane-like vortices, moist processes directly affect the structure of these storms.

scholarly journals Stable Numerical Evaluation of Finite Hankel Transforms and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Manoj P. Tripathi ◽  
B. P. Singh ◽  
Om P. Singh
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Numerical Experiments ◽  
Numerical Evaluation ◽  
Radiation Condition ◽  
Hankel Transform ◽  
Basis Functions ◽  
Infinite Cylinder ◽  
Stable Algorithm ◽  
Hankel Transforms

A new stable algorithm, based on hat functions for numerical evaluation of Hankel transform of order ν>-1, is proposed in this paper. The hat basis functions are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. This leads to a very simple, efficient, and stable algorithm for the numerical evaluation of Hankel transform. The novelty of our paper is that we give error and stability analysis of the algorithm and corroborate our theoretical findings by various numerical experiments. Finally, an application of the proposed algorithm is given for solving the heat equation in an infinite cylinder with a radiation condition.

A 3D Optimized Frequency–Wavenumber (FK), Time–Space Optimized Symplectic (TSOS) Hybrid Method for Teleseismic Wave Modeling

2021 ◽  
Author(s):  
Weijuan Meng ◽  
Dinghui Yang ◽  
Xingpeng Dong ◽  
Jian Ma
Keyword(s):  
High Resolution ◽  
Seismic Wave ◽  
Hybrid Method ◽  
High Efficiency ◽  
Reference Model ◽  
3D Models ◽  
Realistic Model ◽  
High Accuracy ◽  
Memory Requirement ◽  
Time Space

ABSTRACT Although teleseismic waveform tomography can provide high-resolution images of the deep mantle, it is still unrealistic to numerically simulate the whole domain of seismic wave propagation due to the huge amount of computation. In this article, we develop a new three-dimensional hybrid method to address this issue, which couples the modified frequency–wavenumber (FK) method with the 3D time–space optimized symplectic (TSOS) method. First, the FK method, which is used to calculate the semianalytical incident wavefields in the layered reference model, is modified to compute the wavefields efficiently with a significantly low-memory requirement. Second, 3D TSOS method is developed to model the seismic wave propagating in the local 3D heterogeneous domain. The low memory requirement of the modified FK method and the high accuracy of the TSOS method make it feasible to obtain highly accurate synthetic seismograms efficiently. A crust–upper mantle model for P-, SV-, and SH-wave incidences is calculated to benchmark the accuracy and efficiency of the 3D optimized FK-TSOS method. Numerical experiments for 3D models with heterogeneities, undulated discontinuous interfaces, and realistic model in eastern Tibet, illustrate the capability of hybrid method to accurately capture the scattered waves caused by heterogeneities in 3D medium. The 3D optimized FK-TSOS method developed shows low-memory requirement, high accuracy, and high efficiency, which makes it be a promising forward method to further apply to high-resolution mantle structure images beneath seismic array.

A Hybrid Method for Transient Stability Analysis

1997 ◽  
Vol 30 (17) ◽  
pp. 583-587
Author(s):  
Chen Hong ◽  
Xu Jing ◽  
Shan Yuanda
Keyword(s):  
Stability Analysis ◽  
Hybrid Method ◽  
Transient Stability ◽  
Transient Stability Analysis

AUSM-Based High-Order Solution for Euler Equations

2012 ◽  
Vol 12 (4) ◽  
pp. 1096-1120 ◽  
Author(s):  
Angelo L. Scandaliato ◽  
Meng-Sing Liou
Keyword(s):  
Euler Equations ◽  
Splitting Method ◽  
High Order ◽  
Riemann Solvers ◽  
Carbuncle Phenomenon ◽  
Solution Accuracy ◽  
Matrix Vector ◽  
Approximate Riemann Solvers ◽  
Monotonicity Preserving ◽  
High Order Interpolation

AbstractIn this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM+-UP, with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory (WENO-JS) scheme and its variations, and the monotonicity preserving (MP) scheme, for solving the Euler equations. MP is found to be more effective than the three WENO variations studied. AUSM+-UP is also shown to be free of the so-called “carbuncle” phenomenon with the high-order interpolation. The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables, even though they require additional matrix-vector operations. Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison. In addition, four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy. Finally, a measure for quantifying the efficiency of obtaining high order solutions is proposed; the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.

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