High-performance high-resolution semi-Lagrangian tracer transport on a sphere

• Published in: Journal of computational physics Vol. 230; no. 17; pp. 6778 - 6799
• Main Authors: White, J.B., Dongarra, J.J.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.07.2011; Elsevier
• Subjects: Computational techniques; Computer Science; Convergence; Correlation; Cubed sphere; Exact sciences and technology; High resolution; High-performance computing; Mathematical methods in physics; Mathematical models; Nonlinearity; Optimization; Physics; Semi-Lagrangian; Spherical geometry; Tasks; Tracer transport; Tracers; Transport; Cubed sphere; High resolution; Tracer transport; Spherical geometry; High-performance computing; Semi-Lagrangian; Second order; Lagrangian; Third order; Spheres; Calculation methods; Correlations; Models; Calculation; Performance; Time constant; Lagrangian method; Tracers
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2011.05.008

Current climate models have a limited ability to increase spatial resolution because numerical stability requires the time step to decrease. We describe a semi-Lagrangian method for tracer transport that is stable for arbitrary Courant numbers, and we test a parallel implementation discretized on the cubed sphere. The method includes a fixer that conserves mass and constrains tracers to a physical range of values. The method shows third-order convergence and maintains nonlinear tracer correlations to second order. It shows optimal accuracy at Courant numbers of 10–20, more than an order of magnitude higher than explicit methods. We present parallel performance in terms of strong scaling, weak scaling, and spatial scaling (where the time step stays constant while the resolution increases). For a 0.2° test with 100 tracers, the implementation scales efficiently to 10,000 MPI tasks.