Residual-based Discretization Error Estimation for Computational Fluid Dynamics

Discretization error is the largest and most difficult numerical error to estimate for a numerical simulation, and boundary conditions often contribute a significant source of error. Burgers’ equation is used to investigate the formulation of Neumann boundary conditions within the context of discretization error estimation using error transport equations (a residual-based method which solves differential equations governing the transport of numerical error). A strong formulation for the boundary conditions utilizes a computational ghost cell as opposed to a weak formulation which applies the boundary condition directly to the computational domain boundary. The use of the ghost cell allows for error cancelation that results in significantly more accurate discretization error estimation.

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