We should also mention the problem of applying adaptive grid with a finite-difference approximation

About Mathematical Notes quasilinear heat equation in 3D and Stefan problem in permafrost alternating direction method for nonlinear heat equation implicit scheme of variable directions and intermediate boundary conditions implicit scheme of variable directions and intermediate boundary conditions finite-difference approximation of boundary conditions 2 and 3 - second kind for nonlinear heat equation On the application of adaptive static partitioning of the computational domain Computational Geometry algorithms and mathematical calculations constructing voxel grids cylindrical shape Transfer boundary conditions on orthogonal hexahedral grid algorithm excluding conflicts of several geometric shapes in cell hexahedral meshes technique of constructing a three-dimensional geological model based on information about wells with an optional partition of condensation on the end of the fast algorithm for computing the volume of an arbitrary polyhedron ess sobeys portal in 3D Technical Advice Project Template for the CUDA architecture to MS Visual Studio 2008 Troubleshooting space in the user name when you compile the project in Nvidia CUDA Runtime MS Visual Studio Company site
Posted ess sobeys portal on: 05.12.2013
Many software packages for numerical calculations allow users to use a static adaptive (hereinafter, simply adaptive) step in the construction of orthogonal structured hexahedral computational grid. That is, based on my own experience, a user wanting to get a more accurate calculation while not significantly increasing the computation time, such programs may specify the places of the computational domain, which is necessary, in his opinion, to apply more detailed partition (use a smaller step space) as compared to the rest of the computational domain.
When properly used, static adaptive partitioning of the computational domain is a powerful tool in the numerical calculations, increasing their accuracy. However, in the case of abuse of the above option can significantly increase the computation time and accuracy of the calculation will not change significantly. In this paper we present the theoretical advantages and disadvantages of using an adaptive partitioning of the computational domain, and give two examples of numerical calculations of thermal fields in the soil. In the first example, the use of adaptive step is appropriate, and the second is not.
In the numerical solution of unsteady problems the time step is selected from the stability criterion of the numerical scheme. For example, for the numerical solution of heat conduction problem by finite difference approximation of the time step selection criterion has the form:
In the case of adaptive partitioning of the computational domain should be avoided strong step reduction ess sobeys portal in space along some direction in the vicinity of a single node. Since the strong reduction step in the vicinity of one node will not give tangible improvements in the accuracy of calculations in general, but, as follows from (1), will greatly reduce the time step, and hence increase the calculation time.
We should also mention the problem of applying adaptive grid with a finite-difference approximation of differential operators. The problem is that the order of the approximation of differential operators generally decreases. Consider, for example, ess sobeys portal finite-difference ess sobeys portal approximation of the operator. Applying ess sobeys portal the approximation to a standard template, we obtain the following formula:
Despite ess sobeys portal the fact that in general the difference operator is approximated with first-order accuracy, in practice, if not and will differ fundamentally term in (5) is sufficiently small and will not have much impact on the accuracy of the approximation.
Also worth noting is that if the user wants to get a more accurate solution on a small area, then it makes sense to mesh refinement only in this area, instead of thickening the grid throughout the computational domain. In this case, the use of adaptive mesh can significantly reduce the number of nodes of the computational grid, thereby significantly reducing the computation time and memory usage.
Need to use adaptive mesh arises when you need to get the detailed sampling of small objects of complex shape. Using a uniform grid in such cases resulted in an excessive number of nodes, which makes it difficult as building a model for the calculation and further calculations on it.
The computational ess sobeys portal domain contains four boxes, ess sobeys portal and feature an asterisk in the middle. The width and height of the calculated area of 60 m height - 20 m Physical parameters of materials shown in Table 1.
The phase transition temperature in all materials is 0 o C. At the boundaries of the computational domain as a boundary condition specified zero heat flux.
To construct the model described above, a computational grid, using a uniform step in all three coordinate axes. Grid pitch of each coordinate axis - 1.0 m so ra