By Gary A. Glatzmaier
This ebook offers readers with the abilities they should write computing device codes that simulate convection, inner gravity waves, and magnetic box new release within the interiors and atmospheres of rotating planets and stars. utilizing a educating procedure perfected within the lecture room, Gary Glatzmaier starts by way of providing a step by step consultant on find out how to layout codes for simulating nonlinear time-dependent thermal convection in a two-dimensional field utilizing Fourier expansions within the horizontal path and finite modifications within the vertical course. He then describes how you can enforce extra effective and actual numerical tools and extra practical geometries in and 3 dimensions. within the 3rd a part of the publication, Glatzmaier demonstrates the way to comprise extra subtle physics, together with the results of magnetic box, density stratification, and rotation.
Featuring various workouts all through, this is often a great textbook for college students and a vital source for researchers.
- Describes how one can create codes that simulate the inner dynamics of planets and stars
- Builds on simple ideas and straightforward methods
- Shows tips to enhance the potency and accuracy of the numerical methods
- Describes extra suitable geometries and boundary conditions
- Demonstrates tips to contain extra refined physics
Read Online or Download Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation PDF
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This e-book offers readers with the talents they should write laptop codes that simulate convection, inner gravity waves, and magnetic box new release within the interiors and atmospheres of rotating planets and stars. utilizing a instructing technique perfected within the school room, Gary Glatzmaier starts via providing a step by step advisor on the best way to layout codes for simulating nonlinear time-dependent thermal convection in a two-dimensional field utilizing Fourier expansions within the horizontal path and finite variations within the vertical path.
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Extra resources for Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation
An easy way to do this is to print out (to the screen or to a file) the values of these three variables for all n but only for one z-level, at, for example, the mid-depth or one-third depth. ” This is called the critical Rayleigh number, Racrit (n), for mode n. That is, if one sets Ra > Racrit (n) the result will be a “supercritical” solution with amplitudes Tn (z, t), ωn (z, t), and ψn (z, t) that increase exponentially with time. Likewise, setting Ra < Racrit (n) will produce an exponentially decaying “subcritical” solution.
Then the two components of velocity can be calculated via Eqs. 6. Notice also that ∇ψ·v vanishes with the help of Eqs. 6; therefore, contours of constant ψ are tangent to the local v. In addition, ∇ψ has the same amplitude as the velocity; so the local density of a set of contours of ψ (that differ by a constant increment) is proportional to the amplitude of the local fluid velocity. Therefore, plots showing contours of ψ are instantaneous “streamlines” of the flow. 2 HORIZONTAL SPECTRAL DECOMPOSITION The problem is now described by Eqs.
There are also two work arrays, wk1 and wk2, that the subroutine uses. The output solution vector is sol. All of these are one-dimensional arrays with Nz elements. 21) sol(3) = rhs(3) . rhs(4) sol(4) sub(4) dia(4) sup(4) rhs(5) sol(5) sub(5) dia(5) The indices, k = 1 to Nz , correspond to the z-levels (vertical grid points), where the bottom boundary is at k = 1 and the top boundary is at k = Nz . , for k = 2 to (Nz − 1)) corresponds to a different k in Eq. 20. That is, sub(k) = − dia(k) = 1 , ( z)2 nπ a sup(k) = − 2 + 2 , ( z)2 1 , ( z)2 rhs(k) = omg(k, n) , 25 NUMERICAL METHOD and on output sol(k) will be psi(k, n).
Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation by Gary A. Glatzmaier