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Nonlinear Finite-Amplitude Dynamics

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter modifies the numerical code by adding the nonlinear terms to produce finite-amplitude simulations. The nonlinear terms are calculated using a Galerkin method in spectral space. After ... More


ALGORITHMS FOR INCOMPRESSIBLE FLOWS

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0008
Subject:
Mathematics, Numerical Analysis

This chapter presents different ways of formulating the incompressible Navier-Stokes equations based on primitive variables, that is, velocity and pressure, as well as velocity-vorticity algorithms. ... More


Time Integration Schemes

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on time integration schemes, including fourth-order accurate Runge–Kutta and predictor-corrector schemes as well as schemes that allow larger time steps (and therefore fewer ... More


Measurement Uncertainty

D. Brynn Hibbert

in Quality Assurance in the Analytical Chemistry Laboratory

Published in print:
2007
Published Online:
November 2020
ISBN:
9780195162127
eISBN:
9780197562093
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195162127.003.0010
Subject:
Chemistry, Analytical Chemistry

One of the great revolutions in metrology in chemistry has been the understanding of the need to quote an appropriate measurement uncertainty with a result. For some time, a standard deviation ... More


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