Eulerian formulation of transport equations for three-dimensional shock waves in simple elastic solids

1983 ◽  
Vol 13 (3) ◽  
pp. 295-310 ◽  
Author(s):  
T. C. T. Ting ◽  
Yongchi Li
Keyword(s):  
Shock Waves ◽  
Three Dimensional ◽  
Transport Equations ◽  
Elastic Solids ◽  
Eulerian Formulation

Three-Dimensional Imaging through Shock-Waves at Ultra-High Speed.

2018 ◽  
Author(s):  
Yi Chen Mazumdar ◽  
Michael E. Smyser ◽  
Jeffery Dean Heyborne ◽  
Daniel Robert Guildenbecher
Keyword(s):  
Shock Waves ◽  
High Speed ◽  
Three Dimensional ◽  
Three Dimensional Imaging ◽  
Ultra High Speed

The Use of Subgrid Transport Equations in a Three-Dimensional Model of Atmospheric Turbulence

1973 ◽  
Vol 95 (3) ◽  
pp. 429-438 ◽  
Author(s):  
J. W. Deardorff
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Transport Equations ◽  
Subgrid Scale ◽  
Reynolds Stresses ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Truncation Errors ◽  
Subgrid Scales ◽  
Grid Points

A three-dimensional numerical model of turbulence in an atmospheric boundary layer has been revised to utilize subgrid transport equations for the subgrid Reynolds stresses and fluxes rather than subgrid eddy coefficients. It was applied to a daytime boundary layer over heated ground in a region of horizontal area 8km square and 2km deep, utilizing 40×40×40 grid points. The constraints involved in selecting four important subgrid closure constants are discussed in some detail, along with maintenance of realizability on the subgrid scale. The results indicate that the subgrid transport equations produce subgrid Reynolds stresses and fluxes which realistically simulate the transfer of larger scale variance to subgrid scales, provided truncation errors due to advective terms are not too large. They also show the superiority of this method over the use of (nonstability dependent) nonlinear eddy coefficients in maintaining the sharpness of the inversion base which lies above the mixed layer.

Steady-State Formulation for Stress and Distortion of Welds

1994 ◽  
Vol 116 (4) ◽  
pp. 467-474 ◽  
Author(s):  
M. Gu ◽  
J. A. Goldak
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Three Dimensional ◽  
Significant Gain ◽  
Free Boundaries ◽  
Flow Lines ◽  
Eulerian Formulation ◽  
Noticeable Reduction ◽  
Computing Speed ◽  
Lagrangian Frame

A steady state formulation has been developed for thermal stress analysis. It uses features from both the Lagrangian formulation and the Eulerian formulation. The mesh sits on an Eulerian frame but deforms as if in the Lagrangian frame. Therefore, it is suitable for steady state problems with free boundaries. History dependent parameters are integrated along flow lines. A significant gain in computing speed and/or spatial resolution over transient analyses has been achieved together with a noticeable reduction for memory requirements. Numerical results are given for a three-dimensional analysis of edge weld.

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