Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
The origin of spurious solutions in computational electromagnetics
Journal of Computational Physics
Overdetermined Elliptic Systems
Foundations of Computational Mathematics
Completion of overdetermined parabolic PDEs
Journal of Symbolic Computation
Global optimization, level set dynamics, incomplete sensitivity and regularity control
International Journal of Computational Fluid Dynamics
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
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We use ideas related to involutive completion of a system of partial differential equations (PDEs) to formulate computational problems of fluid mechanics. As for the solution of differential algebraic equations, the approach requires solution of extra equations for derivative consequences. The extra calculation cost is negligible whereas the discrete form becomes much simpler to handle. We show that in this way we can quite easily improve the performance of existing solvers. Another interest in this article is the derivation of special solutions of the Navier-Stokes system under incompressibility constraint in cylindrical domains.