scholarly journals A Few Benchmark Test Cases for Higher-Order Euler Solvers

2017 ◽  
Vol 10 (4) ◽  
pp. 711-736 ◽  
Author(s):  
Liang Pan ◽  
Jiequan Li ◽  
Kun Xu
Keyword(s):  
Density Ratio ◽  
Strong Shock ◽  
Kinetic Scheme ◽  
Higher Order ◽  
Two Dimensions ◽  
Test Cases ◽  
Rarefaction Waves ◽  
Shock Interactions ◽  
Large Density Ratio ◽  
Set Up

AbstractThere have been great efforts on the development of higher-order numerical schemes for compressible Euler equations in recent decades. The traditional test cases proposed thirty years ago mostly target on the strong shock interactions, which may not be adequate enough for evaluating the performance of current higher-order schemes. In order to set up a higher standard for the development of new algorithms, in this paper we present a few benchmark cases with severe and complicated wave structures and interactions, which can be used to clearly distinguish different kinds of higher-order schemes. All tests are selected so that the numerical settings are very simple and any higher order scheme can be straightforwardly applied to these cases. The examples include highly oscillatory solutions and the large density ratio problem in one dimensional case. In two dimensions, the cases include hurricane-like solutions; interactions of planar contact discontinuities with asymptotic large Mach number (the composite of entropy wave and vortex sheets); interaction of planar rarefaction waves with transition from continuous flows to the presence of shocks; and other types of interactions of two-dimensional planar waves. To get good performance on all these cases may push algorithm developer to seek for new methodology in the design of higher-order schemes, and improve the robustness and accuracy of higher-order schemes to a new level of standard. In order to give reference solutions, the fourth-order gas-kinetic scheme (GKS) will be used to all these benchmark cases, even though the GKS solutions may not be very accurate in some cases. The main purpose of this paper is to recommend other CFD researchers to try these cases as well, and promote further development of higher-order schemes.

Ghost Fluid Method for Strong Shock Interactions Part 1: Fluid-Fluid Interfaces

AIAA Journal ◽  
2009 ◽  
Vol 47 (12) ◽  
pp. 2907-2922 ◽  
Author(s):  
Shiv Kumar Sambasivan ◽  
H. S. UdayKumar
Keyword(s):  
Strong Shock ◽  
Fluid Interfaces ◽  
Ghost Fluid Method ◽  
Shock Interactions

ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES FOR A MODEL SYSTEM OF THE RADIATING GAS IN TWO DIMENSIONS

2008 ◽  
Vol 18 (04) ◽  
pp. 511-541 ◽  
Author(s):  
WENLIANG GAO ◽  
CHANGJIANG ZHU
Keyword(s):  
Cauchy Problem ◽  
Maximum Principle ◽  
Coupled System ◽  
Model System ◽  
Two Dimensions ◽  
Rarefaction Waves ◽  
Asymptotic Decay ◽  
The Maximum Principle ◽  
The Cauchy Problem ◽  
Asymptotic Decay Rate

In this paper, we consider the asymptotic decay rate towards the planar rarefaction waves to the Cauchy problem for a hyperbolic–elliptic coupled system called as a model system of the radiating gas in two dimensions. The analysis based on the standard L2-energy method, L1-estimate and the monotonicity of profile obtained by the maximum principle.

scholarly journals Deep Learning-Based Image Automatic Assessment and Nursing of Upper Limb Motor Function in Stroke Patients

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Xue Chen ◽  
Yuanyuan Shi ◽  
Yanjun Wang ◽  
Yuanjuan Cheng
Keyword(s):  
Deep Learning ◽  
Upper Limb ◽  
Spatial Location ◽  
Two Dimensions ◽  
Superior Performance ◽  
Coefficient Of Determination ◽  
Automatic Assessment ◽  
Evaluation Task ◽  
Point Data ◽  
Set Up

This paper mainly introduces the relevant contents of automatic assessment of upper limb mobility after stroke, including the relevant knowledge of clinical assessment of upper limb mobility, Kinect sensor to realize spatial location tracking of upper limb bone points, and GCRNN model construction process. Through the detailed analysis of all FMA evaluation items, a unique experimental data acquisition environment and evaluation tasks were set up, and the results of FMA prediction using bone point data of each evaluation task were obtained. Through different number and combination of tasks, the best coefficient of determination was achieved when task 1, task 2, and task 5 were simultaneously used as input for FMA prediction. At the same time, in order to verify the superior performance of the proposed method, a comparative experiment was set with LSTM, CNN, and other deep learning algorithms widely used. Conclusion. GCRNN was able to extract the motion features of the upper limb during the process of movement from the two dimensions of space and time and finally reached the best prediction performance with a coefficient of determination of 0.89.

scholarly journals Nonlinear higher-order spectral solution for a two-dimensional moving load on ice

2009 ◽  
Vol 621 ◽  
pp. 215-242 ◽  
Author(s):  
FÉLICIEN BONNEFOY ◽  
MICHAEL H. MEYLAN ◽  
PIERRE FERRANT
Keyword(s):  
Critical Speed ◽  
Moving Boundary ◽  
Moving Load ◽  
Phase Speed ◽  
Nonlinear Effects ◽  
Higher Order ◽  
Two Dimensions ◽  
Linear Solution ◽  
Nonlinear Solution ◽  
Bernoulli’S Equation

We calculate the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method. The nonlinearity is due to the moving boundary, as well as the nonlinear term in Bernoulli's equation and the elastic plate equation. We compare the nonlinear solution with the linear solution and with the nonlinear solution found by Parau & Dias (J. Fluid Mech., vol. 460, 2002, pp. 281–305). We find good agreement with both solutions (with the correction of an error in the Parau & Dias 2002 results) in the appropriate regimes. We also derive a solitary wavelike expression for the linear solution – close to but below the critical speed at which the phase speed has a minimum. Our model is carefully validated and used to investigate nonlinear effects. We focus in detail on the solution at a critical speed at which the linear response is infinite, and we show that the nonlinear solution remains bounded. We also establish that the inclusion of nonlinearities leads to significant new behaviour, which is not observed in the linear solution.

Leveraging the Cloud for Large-Scale Software Testing – A Case Study

2012 ◽  
pp. 252-279 ◽  
Author(s):  
Anjan Pakhira ◽  
Peter Andras
Keyword(s):  
Large Scale ◽  
Analysis Data ◽  
System Level ◽  
Small Scale ◽  
Test Cases ◽  
Software Life Cycle ◽  
Technical Issues ◽  
Wide Scale ◽  
Set Up

Testing is a critical phase in the software life-cycle. While small-scale component-wise testing is done routinely as part of development and maintenance of large-scale software, the system level testing of the whole software is much more problematic due to low level of coverage of potential usage scenarios by test cases and high costs associated with wide-scale testing of large software. Here, the authors investigate the use of cloud computing to facilitate the testing of large-scale software. They discuss the aspects of cloud-based testing and provide an example application of this. They describe the testing of the functional importance of methods of classes in the Google Chrome software. The methods that we test are predicted to be functionally important with respect to a functionality of the software. The authors use network analysis applied to dynamic analysis data generated by the software to make these predictions. They check the validity of these predictions by mutation testing of a large number of mutated variants of the Google Chrome. The chapter provides details of how to set up the testing process on the cloud and discusses relevant technical issues.

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