Ghost Cell CFD Mesh for Irregular Fluid Boundaries
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Solution Overview
Problem
Current computational fluid dynamics (CFD) models face inaccuracies and increased computational times when modeling fluid dynamic systems with irregularly-shaped boundaries, as Cartesian meshes often fail to perfectly fit these systems, leading to gaps and interference issues that result in unstable solutions and errors.
Innovation Solution
The method employs a ghost-cell approach combined with immersed boundary methods, using a Cartesian mesh with ghost cells that extend outside the system boundaries to accurately model fluid systems, allowing for the use of regular grids without distorting cell shapes, and applying law-of-the-wall functions to determine boundary layer effects without resolving them with the mesh.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If Cartesian meshes are used to model fluid systems with irregularly-shaped boundaries, then the computational simplicity and ease of implementation are improved, but the accuracy and stability of the solution deteriorate due to gaps and interference issues
Solution Approach 1:
The patent introduces ghost cells as intermediary elements that mediate between the Cartesian mesh structure and the irregular system boundaries. These ghost cells act as buffers that fill the gaps between the rectangular mesh and the actual boundary, enabling the simple Cartesian grid to accurately represent complex geometries without requiring mesh distortion or conformal mapping.
Solution Approach 2:
The patent segments the computational domain into interior cells, boundary cells, and ghost cells. This segmentation allows different treatment for different regions: interior cells use standard Cartesian mesh properties, boundary cells are identified and handled specially, and ghost cells are introduced to represent the external region. This segmentation resolves the contradiction by maintaining Cartesian simplicity in the interior while accurately capturing boundary effects.
2Measurement precision
If high cell densities are used to improve the accuracy of fluid system simulations, then the measurement precision is improved, but the computational time and complexity increase excessively
Solution Approach 1:
The patent applies partial action by introducing ghost cells only in the regions where they are needed - specifically at the boundaries and interfaces of the fluid system. Rather than refining the entire mesh uniformly, the ghost cell approach selectively enhances accuracy only where boundary effects are present, avoiding the excessive computational cost of global mesh refinement while maintaining high accuracy at critical locations.
3Measurement precision
If complex geometries are used to accurately represent fluid systems, then the measurement precision is improved, but the device complexity and computational resources required increase
Solution Approach 1:
The patent inverts the traditional approach by not trying to make the mesh conform to the geometry, but instead introducing ghost elements that represent the geometry within the fixed Cartesian mesh framework. Rather than distorting the mesh to fit the boundary, the boundary is represented by adding ghost cells that extend beyond the physical boundary, allowing the simple Cartesian structure to remain while accurately capturing complex geometries.
Data Source
AI summary
A method and apparatus for accessing a data representation of a model associated with a fluid system, the data representation including at least one interior cell and at least one ghost cell, calculating a physical volume value and physical surface area value for at least one interior cell and at least one ghost cell, generating at least one control volume based on one or more physical volume values, generating at least one control surface based on one or more physical surface area values; substituting one or more of the at least one control volume parameter and the at least one surface area for corresponding elements of mathematical conservation equations representative of the fluid system, and solving the mathematical conservation equations representative of the fluid system.