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1 
The geoid for the Baltic countries determined by the least squares modification of Stokes´formulaEllmann, Artu January 2004 (has links)
Precise knowledge of the geoid contributes to the studies ofthe Earths interior, the longterm geophysical processesand to oceanography. An accurate regional geoid model, inparticular, enables the user in many cases to replace thetraditional height determination techniques by faster and morecosteffective GPSlevelling. In regional gravimetric geoid determination, it has becomecustomary to utilize the modified Stokes formula, whichcombines local terrestrial data with a global geopotentialmodel. The Dissertation is devoted to the determination of ahighresolution geoid model for the three Baltic countriesEstonia, Latvia and Lithuania. Six differentdeterministic and stochastic modification methods are tested.These are: Wong and Gore (1969), Vincent and Marsh (1974),Vaníèek and Kleusberg (1987) and the biased, unbiasedand optimum least squares modifications by Sjöberg (1984b,1991, 2003d). Three former methods employ originally theresidual anomaly in Stokesintegral. For the sake ofcomparison these methods are expressed such that the fullgravity anomaly is utilised in all the six methods. The contribution of different error sources for geoidmodelling is studied by means of the expected global meansquare error (MSE). The least squares methods attempt tominimise all relevant error sources in geoid modelling byspecially determined modification parameters. Part of thepresent study contributes to some important computationalaspects of the least squares parameters sn. This study employs the new geopotential model GGM01s, whichis compiled from data of the GRACE twinsatellites. Three sets(one from each country) of GPSlevelling points were used for anindependent evaluation of computed geoid models. Generally, thepostfit residuals from the least squares modifications areslightly smaller (up to 1 cm) than the respective values ofdeterministic methods. This could indicate that the efforts putinto minimization of the global MSE have been advantageous. The geoid model computed by the unbiased LS modificationprovides thebestpostfit statistics and it isthus preferred as the final representation of the joint Balticgeoid. The modification parameters of this model are calculatedfrom the following initial conditions: (1) upper limit of theGGM01s and the modification degree of Stokesfunction areboth set to 67, (2) terrestrial anomaly error variance andcorrelation length are set to 1 mGal2 and 0.1°,respectively, (3) integration cap size is 2°. Thisapproximate geoid model is supplemented by separately computedadditive corrections (the combined topographic and atmosphericeffects and ellipsoidal correction), which completes the geoidmodelling procedures. The new geoid model for the Balticcountries is named BALTgeoid04. The RMS of the GPSlevellingpostfit residuals are as follows: 5.3 cm for the joint Balticgeoid model and 2.8, 5.6 and 4.2 cm for Estonia, Latvia andLithuania, respectively. This fit indicates the suitability ofthe new geoid model for many practical applications. Key words: geoid:Stokesformula, deterministicand stochastic modifications, least squares, additivecorrections, GRACE, Baltic.

2 
Die LadyzhenskayaKonstante in der numerischen Behandlung von StrömungsproblemenKessler, Manuel. January 1900 (has links) (PDF)
Würzburg, Univ., Diss., 2000. / Erscheinungsjahr an der Haupttitelstelle: 2000. Computerdatei im Fernzugriff.

3 
Die LadyzhenskayaKonstante in der numerischen Behandlung von StrömungsproblemenKessler, Manuel. January 1900 (has links) (PDF)
Würzburg, Univ., Diss., 2000. / Erscheinungsjahr an der Haupttitelstelle: 2000. Computerdatei im Fernzugriff.

4 
Numerische Approximation der StokesGleichung mit künstlichen Randbedingungen in 3DRohrsystemenBlazy, Stephan. January 2001 (has links) (PDF)
Paderborn, Universiẗat, Diss., 2001.

5 
Die LadyzhenskayaKonstante in der numerischen Behandlung von StrömungsproblemenKessler, Manuel. January 1900 (has links) (PDF)
Würzburg, Universiẗat, Diss., 2000. / Erscheinungsjahr an der Haupttitelstelle: 2000.

6 
Charakterisierung eines Gebiets durch Spektraldaten eines Dirichletproblems zur StokesgleichungTsiporin, Viktor. January 2004 (has links) (PDF)
Göttingen, Universiẗat, Diss., 2004. / Erscheinungsjahr an der Haupttitelstelle: 2003.

7 
The geoid for the Baltic countries determined by the least squares modification of Stokes´formulaEllmann, Artu January 2004 (has links)
<p>Precise knowledge of the geoid contributes to the studies ofthe Earths interior, the longterm geophysical processesand to oceanography. An accurate regional geoid model, inparticular, enables the user in many cases to replace thetraditional height determination techniques by faster and morecosteffective GPSlevelling.</p><p>In regional gravimetric geoid determination, it has becomecustomary to utilize the modified Stokes formula, whichcombines local terrestrial data with a global geopotentialmodel. The Dissertation is devoted to the determination of ahighresolution geoid model for the three Baltic countriesEstonia, Latvia and Lithuania. Six differentdeterministic and stochastic modification methods are tested.These are: Wong and Gore (1969), Vincent and Marsh (1974),Vaníèek and Kleusberg (1987) and the biased, unbiasedand optimum least squares modifications by Sjöberg (1984b,1991, 2003d). Three former methods employ originally theresidual anomaly in Stokesintegral. For the sake ofcomparison these methods are expressed such that the fullgravity anomaly is utilised in all the six methods.</p><p>The contribution of different error sources for geoidmodelling is studied by means of the expected global meansquare error (MSE). The least squares methods attempt tominimise all relevant error sources in geoid modelling byspecially determined modification parameters. Part of thepresent study contributes to some important computationalaspects of the least squares parameters sn.</p><p>This study employs the new geopotential model GGM01s, whichis compiled from data of the GRACE twinsatellites. Three sets(one from each country) of GPSlevelling points were used for anindependent evaluation of computed geoid models. Generally, thepostfit residuals from the least squares modifications areslightly smaller (up to 1 cm) than the respective values ofdeterministic methods. This could indicate that the efforts putinto minimization of the global MSE have been advantageous.</p><p>The geoid model computed by the unbiased LS modificationprovides thebestpostfit statistics and it isthus preferred as the final representation of the joint Balticgeoid. The modification parameters of this model are calculatedfrom the following initial conditions: (1) upper limit of theGGM01s and the modification degree of Stokesfunction areboth set to 67, (2) terrestrial anomaly error variance andcorrelation length are set to 1 mGal2 and 0.1°,respectively, (3) integration cap size is 2°. Thisapproximate geoid model is supplemented by separately computedadditive corrections (the combined topographic and atmosphericeffects and ellipsoidal correction), which completes the geoidmodelling procedures. The new geoid model for the Balticcountries is named BALTgeoid04. The RMS of the GPSlevellingpostfit residuals are as follows: 5.3 cm for the joint Balticgeoid model and 2.8, 5.6 and 4.2 cm for Estonia, Latvia andLithuania, respectively. This fit indicates the suitability ofthe new geoid model for many practical applications.</p><p><b>Key words: geoid:</b>Stokesformula, deterministicand stochastic modifications, least squares, additivecorrections, GRACE, Baltic.</p>

8 
Stokes operator and stability of stationary navierstokes flows in infinite cylindrical domainsRi, Myong Hwan. Unknown Date (has links)
Techn. University, Diss., 2006Darmstadt.

9 
Finite element solvers and preconditioners for nonrotational and rotational NavierStokes equationsTang, Sinting, 鄧倩婷 January 2013 (has links)
NavierStokes equations (NSE), the governing equations of incompressible ows, and rotational NavierStokes equations (RNSE), which model incompressible rotating ows, are of great importance in many industrial applications. In this thesis, several selected preconditioners for solving NSE are compared and analyzed. These preconditioners are then modified for applying to RNSE.
Understanding the physics behind NSE and RNSE is essential when studying these two equations. The derivation of NSE from the law of conservation of mass and law of conservation of momentum is described. RNSE is obtained by changing the frame of reference of NSE to a rotational frame.
The rotating effect leads to the extra Coriolis force term in RNSE. The equations are then scaled to dimensionless form to eliminate the effect of physical units.
In practice, numerical solution of NSE instead of analytic solution is considered. To apply numerical solvers in this thesis, NSE is discretized by backward differentiation formula in time and finite element method in space. The nonlinear term is linearized by extrapolation. The existence and uniqueness of the finite element solutions to NSE are shown in this thesis. Discretization and linearization result in a system of linear equations which is of saddle point type.
Generalized minimum residual method (GMRES) is applied to solve the saddle point system so as to improve efficiency. GMRES is combined with preconditioning technique to enhance the convergence. In this thesis, three preconditioners, pressure convectiondiffusion (PCD) [18], least squares commutator (LSC) [11] and relaxed dimensional factorization preconditioner (RDF) [4], for nonrotational problems are considered and investigated. The performance of preconditioners is compared in terms of time step dependency, mesh size dependency and Reynolds number (Re) dependency. It is found that PCD shows time step and mesh size independence for small Reynolds number (Re = 500). RDF is the most stable preconditioner among three preconditioners, but it costs slow convergence, which contrasts to the results in [4].
Preconditioners PCD, LSC and RDF are modi_ed to deal with the Coriolis force term in RNSE. Discrete projection method (DPM) [24], an algorithm designed for RNSE, is also considered. This algorithm can also be viewed as a preconditioned iterative method. The time step and Ekman number (Ek) dependency of modi_ed preconditioners and DPM are compared. The numerical results indicates that LSC is the best preconditioner against time step and Ek. DPM is only the second best although it is designed for RNSE. PCD is the worst preconditioner as it shows high Ek dependency. / published_or_final_version / Mathematics / Master / Master of Philosophy

10 
Analysis of the multigrid methodShah, Tasneem Mohammad January 1989 (has links)
No description available.

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