Abstract
The governing equations for shallow water flow on the sphere are formulated in generalized curvilinear coordinates. The various analytic expressions for the differential operators are all mathematically equivalent. However, numerical approximations are not equally effective. The accuracy of high-order finite element discretizations are evaluated using the standard test problems proposed by Williamson et al (1992). The so-called strong conservation formulation is far more accurate and results in standard error metrics that are at least two orders of magnitude smaller than the weak conservation form, Jorgensen (2003), Prusa and Smolarkeiwicz (2003). Moreover, steady state solutions can be integrated much longer without filtering when time-stepping the physical velocities.
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Keywords
- Shallow Water Equation
- Spectral Element Method
- Discontinuous Galerkin Scheme
- Physical Velocity
- Standard Test Problem
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Thomas, S.J., St.-Cyr, A. (2005). On the Accuracy of High-Order Finite Elements in Curvilinear Coordinates. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428848_105
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DOI: https://doi.org/10.1007/11428848_105
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