Multi-grid Computation for Embedded Grid Cells in CFD Models
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Solution Overview
Problem
Existing computational fluid dynamics models, such as MoSES, face inefficiencies when dealing with embedded cells in fluid dynamic systems, particularly in regions of high gradients, as the increased number of cells makes iterations more time-consuming and less efficient, despite the need for precise thermophysical value information.
Innovation Solution
A method and apparatus that iteratively solve transport equations on embedded grid cells and adjacent cells, group embedded grid cells to match the size of other cells, and perform multi-grid computations to average residuals, allowing conventional multi-grid methods to operate effectively on embedded grids, thereby accelerating convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If embedded cells of smaller size are used to obtain more precise thermophysical value information in regions of high gradients, then measurement precision is improved, but productivity deteriorates because each iteration becomes more time consuming
Solution Approach 1:
The computational domain is segmented into multiple grid levels with different resolutions. Embedded cells in regions of high gradients are grouped into composite cells that are treated at coarser grid levels, while maintaining fine resolution at the computational level. This segmentation allows the system to maintain measurement precision in critical regions while improving productivity through multi-grid computation.
Solution Approach 2:
The problem is solved by adding a temporal dimension through multi-grid computation. Instead of solving all fine-grid cells at every iteration, the method uses coarse-grid computations to advance the solution in time, then corrects with fine-grid iterations. This dimensional approach to computation significantly reduces iteration time while maintaining precision.
2Measurement precision
If the number of cells is increased to model regions of high gradients with embedded cells, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The computational model is segmented into multiple grid levels, with embedded cells grouped into composite cells at coarser levels. This segmentation reduces the apparent complexity by organizing fine-grid cells into manageable groups that can be processed at different computational levels, maintaining precision without overwhelming system complexity.
Solution Approach 2:
The computational approach dynamically adapts the level of detail used at different grid levels and iteration stages. Fine-grid resolution is applied only when and where necessary, while coarse-grid computations handle broader regions. This dynamic adjustment optimizes the balance between precision and complexity throughout the computation process.
Data Source
AI summary
Method and apparatus are disclosed for implementing a geometric multi-cell system dynamics model having an embedded grid, the embedded grid having cells with a finer grid size relative to the grid size of other cells. The apparatus includes a digital computer having a computational fluid dynamics model program stored therein, the program having software for iteratively solving transport equations for thermophysical values for the embedded cells and the other cells, and for solving residual equations for the values for each cell using a multi-grid computation method. The program also has other software for computationally manipulating the embedded grid cells to provide composite cells of the same grid size as the other cells and having averaged residual thermophysical values, for allowing the multi-grid computation method to operate on the embedded grid cells.