RESIDUAL-BASED DISCRETIZATION ERROR
ESTIMATION FOR COMPUTATIONAL FLUID
DYNAMICS
Tyrone S. Phillips
Graduate Research Assistant
Department of Aerospace and Ocean
Engineering
Virginia Tech, Blacksburg, Virginia 24061
Email: tphilli6@vt.edu
Advisor: Christopher J. Roy
Associate Professor
Department of Aerospace and Ocean
Engineering
Virginia Tech, Blacksburg, Virginia 24061
Email: cjroy@vt.edu
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.
Phillips
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