| Title: |
Higher-order isospectral time-integration for hydrodynamics on the sphere. |
| Authors: |
Silva, Clauson C. da; Viviani, Milo; Lessig, Christian |
| Source: |
Journal of Computational Dynamics; Apr2026, Vol. 14, p1-14, 14p |
| Subject Terms: |
Time integration scheme; Runge-Kutta formulas; Numerical analysis; Computational fluid dynamics; Incompressible flow; Euler equations; Hydrodynamics; Energy conservation |
| Abstract: |
We investigate the benefits of higher-order time-integration for the quantized formulation of the Euler equations for incompressible fluid flow on the sphere. We show that higher-order isospectral symplectic Runge–Kutta (IsoSyRK) methods are a viable and efficient alternative to the widely used isospectral implicit midpoint method. When implemented using a block matrix approach, higher-order methods allow for effective parallelization and exhibit superior conservation of the Hamiltonian while reducing overall simulation time due to the larger time-step enabled by higher-order methods. We establish this with a series of numerical experiments that compare energy and enstrophy conservation, as well as execution time across integrators of different orders. A qualitative experiment illustrates further benefits of these integrators, showing that their enhanced conservation properties translate into more stable long-time behavior for a simulation starting from a sensitive initial condition. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |