Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  describe a new approach for the purely Eulerian simulation of incompressible fluids. In it, the fluid state is represented by a C 2 -valued wave function evolving under the Schrodinger equation subject to incompressibility constraints. The underlying dynamical system is Hamiltonian and governed by the kinetic energy of the fluid together with an energy of Landau-Lifshitz type. The latter ensures that dynamics due to thin vortical structures, all important for visual simulation, are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized grids. Our implementation uses a simple splitting method for time integration, employing the FFT for Schrodinger evolution as ll as constraint projection. Using a standard penalty method  also allow arbitrary obstacles. The resulting algorithm is simple, unconditionally stable, and efficient. In particular it does not require any Lagrangian techniques for advection or to counteract the loss of vorticity.  demonstrate its use in a variety of scenarios, compare it with experiments, and evaluate it against benchmark tests. A full implementation is included in the ancillary materials.
['Albert Chern', 'Felix Knöppel', 'Ulrich Pinkall', 'Peter Schröder', 'Steffen Weißmann']
I am writing a research paper on a idea Schrödinger's smoke
[{"from": "human", "value": "I am writing a research paper on a idea Schr\u00f6dinger's smoke"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  describe a new approach for the purely Eulerian simulation of incompressible fluids. In it, the fluid state is represented by a C 2 -valued wave function evolving under the Schrodinger equation subject to incompressibility constraints. The underlying dynamical system is Hamiltonian and governed by the kinetic energy of the fluid together with an energy of Landau-Lifshitz type. The latter ensures that dynamics due to thin vortical structures, all important for visual simulation, are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized grids. Our implementation uses a simple splitting method for time integration, employing the FFT for Schrodinger evolution as ll as constraint projection. Using a standard penalty method  also allow arbitrary obstacles. The resulting algorithm is simple, unconditionally stable, and efficient. In particular it does not require any Lagrangian techniques for advection or to counteract the loss of vorticity.  demonstrate its use in a variety of scenarios, compare it with experiments, and evaluate it against benchmark tests. A full implementation is included in the ancillary materials."}]