At the end of the summer after a teacher's recommendation, I contacted using the GPU to calculate the GCM model --- THOR, record the reading process here at the paper and related ideas.
THOR Introduction
THOR in the establishment of the model actually standing on the shoulders of giants GCM, so the author's goal is to develop a model GCM robust and flexible enough to require such a model can not cope with the situation on Earth, but also support the analysis in a variety of planetary conditions. More specific goal is to provide a dynamical core to simulate and help us better understand the atmospheric dynamics and climate characteristics of various planets.
It has the following features
Simulation accuracy is not consistent and depends heavily on the specific conditions of the planet
Suppose minimize impact on physical problems
It should be established for the simulation work instead of relying on the physical picture of the specific issues considered optimization
THOR core consists of two components, namely physical and kinetic core core, wherein the core is to solve the physical, such as convection and radiative transfer equation for a class of physics; kinetic core is made to solve the hydrodynamic equations.
Grid structure
In order to avoid problems in the traditional pole problem latitude and longitude appearing online, meshing models using the icosahedral configurations body. Main reason for selecting the icosahedron is icosahedral polyhedron relative to other quasi-equilibrium with better characteristics (even more than 12 mesh vertices does not exist). But only this amount icosahedron is impossible to meet the required resolution, it is necessary not to increase the number of vertices destruction quasi-uniform grid features premise. There are two ways, one is another iterative methods of non-iterative. Iterative approach is continuously connected to the surface of the icosahedral triangle centered on each side of the split triangles to generate a new surface, and increase the number of vertices. A non-iterative way because they do not facilitate parallel, discard it and the larger adjacent points on the ratio of the longest and shortest distance. Paper given grid point calculated after birth spatial resolution of the overall mesh network and angular resolution. And calculating the flow flux different side of the average method. Finally, to calculate the fluid information between the two successive layers, using a method of Lagrange interpolation.
But this grid needs further improvement value of divergence and gradient precision, here focused on solving the problem of distortion would be placed on the edge of the largest initial icosahedron. To solve this problem, a method of using springs dynamic, the use of a spring-like traction form vertices (all mesh vertices are vertices latest form and connect the spring-like), such as the operation step of the operation moves all vertices 5 ...... distance is less than 10 ends. The authors then used l2 and l (infinite) of the evaluation means to enhance test accuracy and divergence gradient grid calculation, the effect is more significant.
Kinetic equation and estimates
First, when building dynamic model we have actually made some assumptions, but those assumptions may be convenient to study the Earth's environment proposed in the case of other planets may not use, and even affect the accuracy of the model. So to the flexibility of the model, we should try to reduce the number of assumptions. THOR herein discarded model assumptions include static assumptions, i.e. the ratio of eigenvalues scale height and horizontal grid direction is much less than 1; diving wave assumption, we studied that a thickness of the atmosphere is far less than the height center of the planet to study distance; anelastic hypothesis, proposed to ignore elasticity. Although the above assumption is omitted, but this does not mean that all abandoned THOR model assumptions, the first atmosphere is not ionized; second is effective gravitational constant and is along the radial direction. After the above assumptions of choice, the author lists the flow equation of the form. Taking into account the CFL condition, i.e. the time scale such power core should be small enough, the reaction may occur at intervals of time less physical process, and the need for conservation equations are listed, regardless of the phase change of the water component, the equation describes the dry atmosphere. However, due to conservation of the relationship between the kinetic and thermal energy to solve the thermodynamic equation which can not be displayed (process portion of the energy dimension of less than the ranges discussed equation). And in order to obtain the momentum equation, assuming ideal gas is introduced here to establish the relationship between the gas pressure.
Consider again the CFL condition, using the Split-explicit THOR, comprising the Euler time interval into smaller intervals and large intervals of two parts, a small portion of the processing time interval associated acoustic mode information, the time interval is large to address the remaining issues. In THOR, in order to solve a wide range of issues such CFL THOR time interval will be reduced as much as possible to ensure the fastest wave in each direction information is not missed. It is through a large set of small cycles cycle calculation is performed in a long period of time equations in a cycle specific programming stage, while the inner loop once for each cycle the time interval is reduced accordingly and the number of iterations. Finally, when the program and solved by the finite difference discretization in the thickness direction by two top and bottom of the model boundary conditions using a Thomas algorithm.
Numerical dissipation
The intensity depends on the numerical diffusion time simulation of wave damping. THOR an explicit representation dissipation, the amount of a transmission intensity is tunable, generally set large enough to ensure the stability of the model, and does not vary with changes in latitude and longitude. At the same time a problem of concern is the order of divergence operations, due to the low-order divergence operations are usually hot and transmission or delivery molecule has a relationship but this process is not a small-scale model can be used to solve the GCM. It should therefore be possible to use higher order operators. After weighing the calculation amount and accuracy, using the 4th order THOR selected operator, the paper gives the flux equation of the form. And explains the divergence damping is updated on a long time in each small step, other items are spread will be updated on a large time step.
PROFX physical core
This paper describes less, the predicted point is updated by using the variable power core to the results achieved in the Euler equation into the post of the physical core.
GPU implementation
THOR when GPu achieved mainly divided into two parts, the variables are declared in the first portion, the required model, initialization and the application in the host and GPU memory space; and a second portion is a mesh structure configured Model and mathematical operations, and sets the initial conditions of the atmosphere. In the concrete embodiment, the use of parallel execution approach, and the results obtained are returned to the host side. I actually tested this model when I found the model to run on my GTX 1060 card speed is very fast, about an hour's time I got 100 days of data, 100 days out of the model spin-up phase of the external or there are more than 200 days meaningful data, this really is a good achievement too!
Benchmarking
I did not expect it to run sub-atmospheric model as well as the author of THOR are made under test conditions of the Earth and Jupiter hot conditions, the results are basically consistent with the results found and develop a more complete model is given. The validity of THOR.
in conclusion
Of course, it is this model itself!
Finally, as usual, upload a picture to read THOR:
