$L^2$-stability of explicit schemes for incompressible Euler equations
Provides theoretical stability guarantees for numerical schemes in computational fluid dynamics, though the result is incremental as it extends known skew-symmetry arguments.
The paper proves $L^2$-stability conditions for explicit schemes solving incompressible Euler equations, showing stability under $δt \\leq C δx^{2r/(2r-1)}$ for small perturbations.
We present an original study on the numerical stabiliy of explicit schemes solving the incompressible Euler equations on an open domain with slipping boundary conditions. Relying on the skewness property of the non-linear term, we demonstrate that some explicit schemes are numerically stable for small perturbations under the condition $δt\leq C δx^{2r/(2r-1)}$ where $r$ is an integer, $δt$ the time step and $δx$ the space step.