The purpose of code verification is to provide mathematical evidence that a scientific computing software platform is free of bugs in the source code and that the numerical algorithms are consistent. &nbsp;Code verification methodologies range from code-to-code comparisons to comparison to analytical solutions to calculating the observed order of accuracy, the latter providing the most stringent evidence that the numerical algorithms are error-free.&nbsp; The Method of Exact Solutions (MES) and the Method of Manufactured Solutions (MMS) are the currently accepted approaches for calculating the observed order of accuracy. &nbsp;And while both methods are well-established, inherent drawbacks are limiting their utilization by the computational modeling community.&nbsp; For example, the idealized nature of the geometry, material properties, and boundary conditions limits the utility of MES.&nbsp; Meanwhile, the development and solution of complex multi-term differential equations, material properties, and boundary conditions to fully exercise all terms of the model form in all coordinate directions is a roadblock to MMS.&nbsp; To address these challenges, this presentation outlines the Method of Rotated Solutions (MRS), which makes use of coordinate transformations in conjunction with MES to determine the observed order of accuracy.&nbsp; Using Hagen-Poiseuille flow as an example, it will be shown how a properly applied coordinate transformation results in non-zero values for all degrees of freedom and their derivatives in the various coordinate directions (including those terms whose values may have been identically zero in the exact solution).Hagen-Poiseuille flow refers to pressure-driven flow in a circular pipe.&nbsp; The flow solution is uniaxial in nature, i.e. there is a non-zero velocity component in the axial direction and the radial and azimuthal velocity components are identically zero.&nbsp; This solution has limited applicability in code verification because all inertial terms and all but one of the viscous terms in the Navier-Stokes are zero.&nbsp; Rotating the pipe centerline such that it is at a 45-degree angle relative to the x, y, and z-axes expands the scope of this simple analytical solution to cover all terms in the Navier-Stokes equations.&nbsp; An investigation comparing and contrasting the observed order of accuracy results using the MES and MRS approaches will be reviewed.&nbsp;In summary, MRS provides a convenient and accessible method for establishing the accuracy of numerical algorithms and also expedites their solution because of the simplified nature of the exact solutions.&nbsp; Indeed, a fundamental advantage of this approach is that the observed order of accuracy may be determined using more familiar and compact analytical solutions.

The Method of Rotated Solutions as a Fast and Efficient Method of 3-D Cfd Code Verification

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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