The velocity decomposition method for second-order accuracy in stochastic parcel simulations

2012 ◽  
Vol 47 ◽  
pp. 160-170 ◽  
Author(s):  
Philipp Pischke ◽  
Diana Cordes ◽  
Reinhold Kneer
Keyword(s):  
Decomposition Method ◽  
Second Order ◽  
Order Accuracy ◽  
Velocity Decomposition

scholarly journals Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Nemat Dalir
Keyword(s):  
Fluid Mechanics ◽  
Analytical Solutions ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Differential Operators ◽  
Second Order ◽  
Nonlinear Pdes ◽  
Initial Value ◽  
Exact Analytical Solutions ◽  
First Order

Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.

scholarly journals A New Nutation Model Of Nonrigid Earth With Ocean And Atmosphere

2000 ◽  
Vol 180 ◽  
pp. 242-247
Author(s):  
Cheng-li Huang ◽  
Wen-jing Jin ◽  
Xing-hao Liao
Keyword(s):  
Transfer Functions ◽  
Second Order ◽  
Earth Model ◽  
Surface Boundary ◽  
Complex Frequency ◽  
Order Accuracy ◽  
Complex Scalar ◽  
Motion Equations ◽  
Surface Boundary Conditions ◽  
Nutation Series

AbstractBy integrating the truncated complex scalar gravitational motion equations for an anelastic, rotating, slightly elliptical Earth, the complex frequency dependent Earth transfer functions are computed directly. Unlike the conventional method, the effects of both oceanic loads and tidal currents are included via outer surface boundary conditions, all of which are expanded to second order in ellipticity. A modified ellipticity profile in second order accuracy for the non-hydrostatic Earth is obtained from Clairaut’s equation and the PREM Earth model by adjusting both the ellipticity of the core-mantle boundary and the global dynamical ellipticity to modern observations. The effects of different Earth models, anelastic models, and ocean models are computed and compared. The atmospheric contributions to prograde annual, retrograde annual and retrograde semiannual nutation are also included as oceanic effects. Finally, a complete new nutation series of more than 340 periods, including in-phase and out-of-phase parts of longitude and obliquity terms, for a more realistic Earth, is obtained and compared with other available nutation series and observations.

Two-Dimensional Equations of Second Order Accuracy for a Multilayered Plate with Orthotropic Layers

2018 ◽  
Vol 63 (11) ◽  
pp. 471-475 ◽  
Author(s):  
N. F. Morozov ◽  
A. K. Belyaev ◽  
P. E. Tovstik ◽  
T. P. Tovstik
Keyword(s):  
Second Order ◽  
Two Dimensional ◽  
Multilayered Plate ◽  
Order Accuracy

A MODIFIED SUB-CELL-FIX METHOD FOR RE-INITIALIZATION OF LEVEL-SET DISTANCE FUNCTION AND ITS DEPENDENCE TESTS ON GRID STRETCHING

2010 ◽  
Vol 24 (15) ◽  
pp. 1615-1629
Author(s):  
MING BO SUN ◽  
XUE SONG BAI ◽  
WEI DONG LIU ◽  
JIAN HAN LIANG ◽  
ZHEN GUO WANG
Keyword(s):  
Level Set ◽  
Distance Function ◽  
Second Order ◽  
Test Cases ◽  
Local Curvature ◽  
Order Accuracy ◽  
Zero Level ◽  
Numerical Errors ◽  
Satisfactory Performance ◽  
Set Distance

The sub-cell-fix (SCF) method proposed by Russo and Smereka3 computes the distance function of the cells adjacent to the zero level-set without disturbing the original zero level-set. A modified sub-cell-fix scheme independent of local curvature is developed in this paper, which makes use of a combination of the points adjacent to zero level-set surfaces and preserves the interface in a second-order accuracy. The new sub-cell-fix scheme is capable of handling large local curvature, and as a result it demonstrates satisfactory performance on several challenging test cases. The limitations of the modified scheme on stretched grids are tested and it is found that the highly stretched grid causes large numerical errors, and needs further assessment and modification.

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