Non-weak/strong solutions in gas dynamics: aC11p-version STLSFEF in Lagrangian frame of reference using?, u, p primitive variables

2001 ◽  
Vol 53 (5) ◽  
pp. 1025-1050 ◽  
Author(s):  
K. S. Surana ◽  
David G. Van Dyne
Keyword(s):  
Gas Dynamics ◽  
Strong Solutions ◽  
Frame Of Reference ◽  
Lagrangian Frame ◽  
Primitive Variables

A New Theoretical and Computational Framework for Computing Solution of Higher Classes With Application to Gasdynamics in Eulerian Frame of Reference

2001 ◽  
Author(s):  
K. S. Surana ◽  
Ali R. Ahmadi
Keyword(s):  
Differential Equations ◽  
Convergence Rates ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Integral Form ◽  
Frame Of Reference ◽  
Mathematical Framework ◽  
Partial Differential ◽  
One Dimensional

Abstract This paper presents a new computational strategy along with a computational and mathematical framework for computing non-weak numerical solutions of stationary and time dependent partial differential equations. This approach utilizes strong form of the governing differential equations (GDE) and least squares approach in constructing the integral form. This new proposed approach is applied to one dimensional transient gasdynamics equation in Eulerian frame of reference using ρ, u, T as dependent variables. The currently used finite element approaches seek convergence of a solution in a fixed order space by h, p, or hp-adaptive processes. The fundamental point of departure in the proposed approach is that we seek the convergence of the computed converged solution over the spaces of different orders containing the basis functions. With this approach, dramatically higher convergence rates than those obtained for h, p, or hp-processes are achievable and the sequence of progressively converged solutions over the spaces of progressively increasing order in fact converge to the strong solution (analytical or theoretical) of the partial differential equation. It is demonstrated using one-dimensional transient Navier-Stokes equations for compressible fluid flow in Eulerian frame of reference, that in the presence of physical diffusion and dissipation, our computed solutions have exactly the same characteristics as the strong solutions. Riemann shock tube is used as a model problem.

scholarly journals Predictability of Precipitation from Continental Radar Images. Part V: Growth and Decay

2012 ◽  
Vol 69 (11) ◽  
pp. 3336-3349 ◽  
Author(s):  
Basivi Radhakrishna ◽  
Isztar Zawadzki ◽  
Frédéric Fabry
Keyword(s):  
Probability Density Function ◽  
Scale Dependence ◽  
Frame Of Reference ◽  
Time Interval ◽  
Dependence Analysis ◽  
Two Dimensional ◽  
Continental Scale ◽  
Radar Images ◽  
Lagrangian Frame ◽  
The U.S

Abstract In a Lagrangian frame of reference, the accuracy of rainfall systems predicted by nowcasting algorithms can be improved by incorporating the growth and decay of the rainfall. The scale dependence of predictability of growth and decay of continental-scale precipitating systems is studied with the help of the U.S. national radar composites. The growth and decay of precipitating systems is estimated in a time interval τ by correcting the precipitation image for advection and rotation at time t + τ with respect to the precipitation image at time t and then subtracting the former from the latter. Results show that the two-dimensional correlation of growth and decay has an elliptical structure, indicating that growth and decay is nonisotropic. The probability density function of precipitation intensities and of growth and decay follows a Gaussian distribution. The scale-dependence analysis of growth and decay patterns indicates that the growth and decay of rainfall may be predictable up to about 2 h for scales larger than 250 km.

scholarly journals LAGRANGIAN CORRELATION AND SPECTRA IN 2D TURBULENCE

2014 ◽  
Vol 34 ◽  
pp. 1460378
Author(s):  
HUA XIA
Keyword(s):  
Kinetic Energy ◽  
Transport Properties ◽  
Single Particle ◽  
Multiple Scales ◽  
Frame Of Reference ◽  
Particle Displacement ◽  
Chaotic Flow ◽  
Developed Turbulence ◽  
Single Scale ◽  
Lagrangian Frame

Transition from chaotic flow to turbulent flow is investigated in both the Eulerian and Lagrangian frame of reference. Eulerian spectra of the kinetic energy of the flow show the development of a hierarchy of scales, generation of a broad k-5/3 spectral range in developed turbulence. In the Lagrangian frame, single particle displacement is dominant by multiple scales for the chaotic flow. In fully developed turbulence, one single scale determines the transport properties, which is related to the most persistent scale in the system, the forcing scale.

Computations of Solutions of Higher Classes of Gasdynamics Equations in Lagrangian Frame of Reference Using a New Theoretical and Computational Framework

2001 ◽  
Author(s):  
K. S. Surana ◽  
Ali R. Ahmadi
Keyword(s):  
Differential Equations ◽  
Convergence Rates ◽  
Stokes Equations ◽  
Least Squares Method ◽  
Frame Of Reference ◽  
Navier Stokes ◽  
Partial Differential ◽  
Computational Framework ◽  
One Dimensional ◽  
Lagrangian Frame

Abstract In this paper we present and utilize a new theoretical and computational framework for computing solutions of higher classes of one dimensional transient Navier-Stokes partial differential equations in Lagrangian frame of reference using ρ, u, T variables. The approach utilizes ‘strong form’ of the governing differential equations (GDEs) and least squares method in constructing integral form. The currently used finite element approaches seek convergence of a solution in a fixed order space by h, p, or hp-adaptive processes. The fundamental point of departure in the proposed approach is that we seek the convergence of the computed converged solution over the spaces of different orders containing the basis functions. With this approach, dramatically higher convergence rates than those obtained for h, or hp-processes are achievable and the sequence of progressively converged solutions over the spaces of progressively increasing order in fact converge to the strong solution (analytical or theoretical) of the partial differential equation. It is demonstrated using one-dimensional transient Navier-Stokes equations for compressible fluid flow in Lagrangian frame of reference in ρ, u, T that in the presence of physical diffusion and dissipation, our computed converged solutions have exactly the same characteristics as the strong solutions. Compression of air in a rigid cylinder is used as the model problem.

Supernovae and interstellar gas dynamics

1967 ◽  
Vol 31 ◽  
pp. 117-119
Author(s):  
F. D. Kahn ◽  
L. Woltjer
Keyword(s):  
Lower Limit ◽  
High Velocity ◽  
Gas Dynamics ◽  
Interstellar Cloud ◽  
Interstellar Gas ◽  
Random Motions ◽  
Relativistic Particles

The efficiency of the transfer of energy from supernovae into interstellar cloud motions is investigated. A lower limit of about 0·002 is obtained, but values near 0·01 are more likely. Taking all uncertainties in the theory and observations into account, the energy per supernova, in the form of relativistic particles or high-velocity matter, needed to maintain the random motions in the interstellar gas is estimated as 1051·4±1ergs.

Replication of Bacteriophage 186 DNA

1972 ◽  
Vol 30 ◽  
pp. 194-195
Author(s):  
Dhruba K. Chattoraj ◽  
Ross B. Inman
Keyword(s):  
Electron Microscopy ◽  
Dna Replication ◽  
Frame Of Reference ◽  
Dna Molecules ◽  
E Coli ◽  
Phage Dna ◽  
Partial Denaturation

Electron microscopy of replicating intermediates has been quite useful in understanding the mechanism of DNA replication in DNA molecules of bacteriophage, mitochondria and plasmids. The use of partial denaturation mapping has made the tool more powerful by providing a frame of reference by which the position of the replicating forks in bacteriophage DNA can be determined on the circular replicating molecules. This provided an easy means to find the origin and direction of replication in λ and P2 phage DNA molecules. DNA of temperate E. coli phage 186 was found to have an unique denaturation map and encouraged us to look into its mode of replication.

Die Spezifität von Begabungsüberzeugungen als Determinante des verbalen und mathematischen Begabungsselbstkonzepts

2002 ◽  
Vol 16 (2) ◽  
pp. 87-97 ◽  
Author(s):  
Jens Möller ◽  
Britta Pohlmann ◽  
Lilian Streblow ◽  
Julia Kaufmann
Keyword(s):  
Reference Model ◽  
Frame Of Reference ◽  
External Frame

Zusammenfassung: Das I/E-Modell (“Internal/External Frame of Reference Model”) von Marsh (1986) postuliert, dass Schülerinnen und Schüler dimensionale Vergleiche der eigenen Leistungen in einem Fach mit den Leistungen in einem anderen Fach anstellen. Diese Vergleiche führen dazu, dass z. B. Schüler mit guten Leistungen in Mathematik ihre verbalen Fähigkeiten niedriger einschätzen. Gegenstand dieser Untersuchung mit N = 1114 Probanden ist die Frage, ob die Überzeugungen von Personen zum Zusammenhang von mathematischer und verbaler Begabung die Effekte dimensionaler Vergleiche moderieren. Analysen zeigten die Bedeutung der Begabungsüberzeugungen der Schülerinnen und Schüler: Negative Zusammenhänge zwischen den Fachleistungen in einem Fach und dem akademischen Selbstkonzept in einem anderen Fach ergaben sich insbesondere für Personen, die annehmen, dass Begabung domänenspezifisch ist, man also entweder mathematisch oder sprachlich begabt ist. Für Schüler mit eher wenig spezifischer Begabungsüberzeugung ergaben sich geringere Effekte dimensionaler Vergleiche.

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