Ghost cells

Definition

Ghost cells are auxiliary computational cells that are used in numerical methods to extend the domain of the simulation and facilitate boundary condition handling. These cells are not part of the physical domain but help in approximating the values at the boundaries or interfaces, making the implementation of numerical schemes more efficient and accurate.

5 Must Know Facts For Your Next Test

1. Ghost cells are essential for implementing boundary conditions in numerical simulations without directly modifying the original computational grid.
2. They allow for better representation of physical phenomena occurring at the boundaries, improving overall solution accuracy.
3. In finite volume methods, ghost cells can be used to compute fluxes across boundaries, making the solution process more efficient.
4. The number of ghost cells needed depends on the order of accuracy of the numerical scheme being employed.
5. Ghost cells are particularly useful when dealing with complex geometries or moving boundaries, as they simplify the implementation of boundary conditions.

Review Questions

• How do ghost cells assist in implementing boundary conditions in numerical simulations?
  • Ghost cells serve as an extension of the computational domain, allowing numerical methods to effectively handle boundary conditions. By populating these auxiliary cells with appropriate values derived from the physical domain, simulations can better approximate behavior at the edges. This method avoids complications associated with directly modifying the main grid while ensuring that the solution remains stable and accurate.
• Discuss the role of ghost cells in enhancing the accuracy of finite volume methods.
  • In finite volume methods, ghost cells play a crucial role in calculating fluxes across control volume boundaries. By providing values that mimic what would occur at actual boundaries, they enable more precise flux calculations and improve overall solution quality. This is especially important for ensuring mass and energy conservation within each control volume, leading to more reliable results in simulations.
• Evaluate how ghost cells can impact the computational efficiency and complexity of simulations involving complex geometries.
  • The inclusion of ghost cells can significantly enhance computational efficiency when simulating complex geometries. By simplifying boundary condition implementation, they reduce the need for elaborate adjustments to the computational grid, saving time and resources. However, they can also introduce complexity in terms of how data is managed across these extended regions, requiring careful consideration of how values are propagated between ghost and real cells to maintain simulation fidelity.

Related terms

Boundary Conditions: Constraints used in numerical simulations to define the behavior of a physical system at its boundaries.

Finite Volume Method: A numerical technique used to solve partial differential equations by dividing the domain into a finite number of control volumes.

Staggered Grid: A grid arrangement where different variables are stored at different locations, often used to improve numerical stability and accuracy.