Mesh adaptation using different error indicators for the Euler equations

“…The work of Zhang et al [10][11][12][13] appears to be the most promising for practical application. Their predicted error distributions were in excellent agreement with exact error distributions for the problems considered.…”

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confidence: 96%

“…Major investigations of ETE models in one and two dimensions have been made by Qin et al [3][4][5][6][7], Celik et al [8,9], and Zhang et al [10][11][12][13]. Van Straalen et al [14] and Wilson and Stern [15] have also explored the concept.…”

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confidence: 99%

Error Quantification for Computational Aerodynamics Using an Error Transport Equation

Cavallo

Sinha

2007

Journal of Aircraft

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Error quantification in computational fluid dynamics is a subject of increasing interest and research. Although solution verification is conventionally performed using systematic grid refinement, Richardson extrapolation can be restrictive in its applicability, possibly requiring more than three grids to establish monotonic behavior. Ultimately, a single grid error estimation method may prove of greater utility for practical application in computational aerodynamics. In this work, an error transport equation is implemented in a three-dimensional upwind unstructured Navier-Stokes solver. An approach for deriving errors in related quantities of interest from the solution of the error transport equation is presented. Error quantification is demonstrated in two and three dimensions for aerodynamic flows where experimental data are available for comparison. Predicted error bars are found to contain fine grid solutions, test data, and the results of Richardson extrapolation. Furthermore, the error transport equation provides meaningful error quantification for aerodynamic coefficients in cases where Richardson extrapolation cannot be applied. Nomenclatureverticeŝ n = unit vector normal to boundary surface P = pressure p = order of convergence exponent Q = conserved variable vector R = error transport equation residual vector R = derived result r = refinement ratiô t = unit vector tangential to boundary surface U = velocity magnitude u, v, w = velocity components V = volume x m , y m , z m = coordinates of moment center = angle of attack = ratio of specific heats F = upwind Roe flux vector f = upwind Roe flux in one dimension t = time step x, y = grid spacings " = error transport equation solution vector " = error = viscosity = density = shear stress Subscripts extrap = extrapolated i = grid point n = normal node REF = reference t = turbulent w = wall node x, y, z = components in the x, y, and z directions 1 = freestream Superscripts h = discretized solution of mesh width h L = left state n = time level R = right state

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“…Such indicators are relatively simple to evaluate and have been analyzed in the past for steady problems. 23 The approximation error can be estimated in various ways. One method for a DG discretization is to consider the inter-element jumps of the solution, an idea that has been considered previously for shock-capturing purposes.…”

Section: Alternative Adaptive Indicatorsmentioning

confidence: 99%

Output-Based Space-Time Mesh Adaptation for Unsteady Aerodynamics

Luo

Fidkowski

2011

49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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An adjoint-based output error estimation algorithm is presented for unsteady problems discretized on static meshes with a space-time discontinuous Galerkin finite element method. An approximate factorization technique is used to solve both the forward and the discrete adjoint problems. A space-time anisotropy measure based on projection of the adjoint solution is used to attribute the error to spatial or temporal resolution. This measure drives a fixed-growth adaptive strategy that employs hanging-node refinement in the spatial domain and slab bisection in the temporal domain. Adaptive results for convection-dominated flows in two dimensions, including those governed by the compressible Navier-Stokes equations, demonstrate the effectivity of the output error estimate and the degree-of-freedom benefits of output-based adaptation compared to uniform space-time refinement and to cheaper heuristic indicators.

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Mesh adaptation using different error indicators for the Euler equations

Cited by 18 publications

References 11 publications

Output-based space–time mesh adaptation for the compressible Navier–Stokes equations

Output-based space–time mesh adaptation for the compressible Navier–Stokes equations

Error Quantification for Computational Aerodynamics Using an Error Transport Equation

Output-Based Space-Time Mesh Adaptation for Unsteady Aerodynamics

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