Details

Autor(en) / Beteiligte

• Dobrev, V.
• Kolev, Tz
• Kuzmin, D.
• Rieben, R.
• Tomov, V.

Titel

Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

Ist Teil von

• Journal of computational physics, 2018-03, Vol.356 (C), p.372-390

Ort / Verlag

Cambridge: Elsevier Inc

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Elsevier ScienceDirect Journals Complete

Beschreibungen/Notizen

• We present a new predictor-corrector approach to enforcing local maximum principles in piecewise-linear finite element schemes for the compressible Euler equations. The new element-based limiting strategy is suitable for continuous and discontinuous Galerkin methods alike. In contrast to synchronized limiting techniques for systems of conservation laws, we constrain the density, momentum, and total energy in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum gradients are adjusted to incorporate the irreversible effect of density changes. Antidiffusive corrections to bounds-compatible low-order approximations are limited to satisfy inequality constraints for the specific total and kinetic energy. An accuracy-preserving smoothness indicator is introduced to gradually adjust lower bounds for the element-based correction factors. The employed smoothness criterion is based on a Hessian determinant test for the density. A numerical study is performed for test problems with smooth and discontinuous solutions. •Bounds-preserving sequential limiting of conserved products.•Positivity preservation for the pressure and internal energy.•Closed-form expressions for element-based correction factors.•No linearization errors, no need for additional postprocessing.•Accuracy-preserving limiters based on a second derivative test.