Invariant Discretization Schemes for the Shallow-Water Equations

Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem

(2011) Alexander Bihlo et al.   JOURNAL OF MATHEMATICAL PHYSICS

A new construction for invariant numerical schemes using moving frames

(2010) Marx Chhay et al.   COMPTES RENDUS MECANIQUE

Comparison of some Lie-symmetry-based integrators

(2010) M. Chhay et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Phase Space Volume Conservation under Space and Time Discretization Schemes for the Shallow-Water Equations

(2010) Matthias Sommer et al.   MONTHLY WEATHER REVIEW

Symmetries and exact solutions of the rotating shallow-water equations

(2009) A. A. CHESNOKOV   EUROPEAN JOURNAL OF APPLIED MATHEMATICS

Lie symmetries and exact solutions of the barotropic vorticity equation

(2009) Alexander Bihlo et al.   JOURNAL OF MATHEMATICAL PHYSICS

A conservative scheme for the shallow-water system on a staggered geodesic grid based on a Nambu representation

(2009) Matthias Sommer et al.   QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY

Adaptivity with moving grids

(2009) Chris J. Budd et al.   ACTA NUMERICA

Invariantization of the Crank–Nicolson method for Burgers’ equation

(2007) Pilwon Kim   PHYSICA D-NONLINEAR PHENOMENA