Relinearization of the error transport equations for arbitrarily high-order error estimates

Tyson, William C.; Yan, Guoying; Roy, Christopher J.; Ollivier‐Gooch, Carl

doi:10.1016/j.jcp.2019.108867

Cited by 11 publications

(3 citation statements)

References 27 publications

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“…The ETE can be solved taking the new truncation error estimate as the source term. This procedure can be performed iteratively to get a better discretization error estimate 13,16 . The process was named relinearization since it was initially applied only to linearized ETE and the ETE is relinearized about the corrected solution at each of the iterative step.…”

Section: Iterative Correction For the Etementioning

confidence: 99%

“…This procedure can be performed iteratively to get a better discretization error estimate. 13,16 The process was named relinearization since it was initially applied only to linearized ETE and the ETE is relinearized about the corrected solution at each of the iterative step. For this work, the technique is also applied to the nonlinear ETE where the solution is corrected iteratively without the relinearization process.…”

Section: Iterative Correction For the Etementioning

confidence: 99%

“…Previous works have discussed in detail the implementation of the ETE for finite-volume schemes. [12][13][14][15][16] However, there has been limited research on the behavior of the ETE for turbulent flow. For turbulent flow, it is usually hard to find an exact solution.…”

Section: Introductionmentioning

confidence: 99%

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Iterated discretization error transport equations for laminar and turbulent flows

Wang

Xue

Roy

2022

Numerical Methods in Fluids

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The focus of this work is on discretization error estimation for finite‐volume schemes using iterated forms of the linear and nonlinear error transport equations. The accuracy of the discretization error estimates is studied by applying the error estimates as corrections to the primal problem and calculating the observed order of accuracy of the corrected solution. The test cases used in this work include two‐dimensional Cross Term Sinusoidal manufactured solutions for laminar flow and turbulent flow modeled by the Spalart–Allmaras and Menter's k−ω Shear Stress Transport model and a boundary layer manufactured solution for the Spalart–Allmaras model. The discretization error estimates of the linearized error transport equations and the nonlinear error transport equations are compared. Higher‐order accurate corrected solutions have been obtained which shows that the discretization error estimates are sufficiently accurate.

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Section: Iterative Correction For the Etementioning

confidence: 99%

Section: Iterative Correction For the Etementioning

confidence: 99%