2017/12/19 by Jonas Kusch, Kusch, Jonas, Graham W. Alldredge +3
Earth and Planetary Sciences · Engineering · #35L65 #35R60 #65M08 #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1712.06966
openalex publication_date 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using standard intrusive techniques when solving hyperbolic conservation laws\nwith uncertainties can lead to oscillatory solutions as well as nonhyperbolic\nmoment systems. The Intrusive Polynomial Moment (IPM) method ensures\nhyperbolicity of the moment system while restricting oscillatory over- and\nundershoots of specified bounds. In this contribution, we derive a second-order\ndiscretization of the IPM moment system which fulfills the maximum principle.\nThis task is carried out by investigating violations of the specified bounds\ndue to the errors from the numerical optimization required by the scheme. This\nanalysis gives weaker conditions on the entropy that is used, allowing the\nchoice of an entropy which enables choosing the exact minimal and maximal value\nof the initial condition as bounds. Solutions calculated with the derived\nscheme are nonoscillatory while fulfilling the maximum principle. The\nsecond-order accuracy of our scheme leads to significantly reduced numerical\ncosts.\n