Well-balanced Preserving of CCWENO-type High Order Entropy Stable Schemes for Shallow Water Equations
The shallow water equations with source term have steady-state solution.The numerical scheme for solving this kind of equations must have well-balanced property,otherwise it will cause oscillation.For the bottom-non-flat shallow water with source term,this paper studies the well-balanced property of the high order compact central weighted essentially non-oscillatory(CCWENO)entropy stable scheme,and proves its well-balanced property.The theory is verified by one-and two-dimensional numerical examples.The numerical results show that the high order CCWENO scheme has the well-balanced property and can accurately capture the small perturbation of the solution even based on the coarse grid.
well-balancedentropy stable schemeshallow water equationsCCWENO reconstructionhydrostatic equilibrium state
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