Abstract
We formulate a fully discrete finite difference numerical method to approximate the incompressible Euler equations and prove that the sequence generated by the scheme converges to an admissible measure valued solution. The scheme combines an energy conservative flux with a velocity-projection temporal splitting in order to efficiently decouple the advection from the pressure gradient. With the use of robust Monte Carlo approximations, statistical quantities of the approximate solution can be computed. We present numerical results that agree with the theoretical findings obtained for the scheme.
Highlights
We formulate a fully discrete finite difference numerical method to approximate the incompressible Euler equations and prove that the sequence generated by the scheme converges to an admissible measure valued solution
We consider the incompressible Euler equations, which model the motion of an inviscid, Newtonian fluid
Our aim is to propose and analyse a variant of the finitedifference projection methods, and prove that it generates sequences that converge to an admissible measure valued solutions of the incompressible Euler equations
Summary
We consider the incompressible Euler equations, which model the motion of an inviscid, Newtonian fluid. These equations can be written as ut + div(u ⊗ u) + ∇p = 0, on D × [0, T ] =: D × I,. Incompressible Euler equations are a fundamental building block of fluid dynamics, and are considered a good model for flows with very low Mach number and high Reynolds number [23]. Their mathematical and numerical understanding is still incomplete. We summarise the main results about Euler equations
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