arXiv subjects

Erwan Deriaz

Publications and source records attributed to Erwan Deriaz.

4 recordsLinked to original sources

arXiv2011

Stability conditions for the numerical solution of convection-dominated problems with skew-symmetric discretizations

This paper presents original and close to optimal stability conditions linking the time step and the space step, stronger than the CFL criterion: $δt\leq Cδx^α$ with $α=\frac{2r}{2r-1}$, $r$ an integer, for some numerical schemes we produce, when solving convection-dominated problems. We test this condition numerically and prove that it applies to nonlinear equations under smoothness assumptions.

math.NA↗

arXiv2007

$L^2$-stability of explicit schemes for incompressible Euler equations

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.

math.NA↗

arXiv2007

Shannon wavelet approximations of linear differential operators

Recent works emphasized the interest of numerical solution of PDE's with wavelets. In their works, A.Cohen, W.Dahmen and R.DeVore focussed on the non linear approximation aspect of the wavelet approximation of PDE's to prove the relevance of such methods. In order to extend these results, we focuss on the convergence of the iterative algorithm, and we consider different possibilities offered by the wavelet theory: the tensorial wavelets and the derivation/integration of wavelet bases. We also investigate the use of wavelet packets. We apply these extended results to prove in the case of the Shannon wavelets, the convergence of the Leray projector algorithm with divergence-free wavelets.

math.NA↗

arXiv2005

Divergence-free Wavelets for Navier-Stokes

In this paper, we investigate the use of compactly supported divergence-free wavelets for the representation of the Navier-Stokes solution. After reminding the theoretical construction of divergence-free wavelet vectors, we present in detail the bases and corresponding fast algorithms for 2D and 3D incompressible flows. In order to compute the nonlinear term, we propose a new method which provides in practice with the Hodge decomposition of any flow: this decomposition enables us to separate the incompressible part of the flow from its orthogonal complement, which corresponds to the gradient component of the flow. Finally we show numerical tests to validate our approach.

math.NA↗