Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
On a class of Padé finite volume methods
Journal of Computational Physics
Second-order sign-preserving conservative interpolation (remapping) on general grids
Journal of Computational Physics
High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations
Journal of Computational Physics
The repair paradigm and application to conservation laws
Journal of Computational Physics
A finite volume formulation of compact central schemes on arbitrary structured grids
Journal of Computational Physics
Journal of Computational Physics
The monotonic Quartic Spline Method (QSM) for conservative transport problems
Journal of Computational Physics
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A hierarchy of one-dimensional high-order remapping schemes is presented and their performance with respect to accuracy and convergence rate investigated. The schemes are also compared based on remapping experiments in closed domains. The piecewise quartic method (PQM) is presented, based on fifth-order accurate piecewise polynomials, and is motivated by the need to significantly improve hybrid coordinate systems of ocean climate models, which require the remapping to be conservative, monotonic and highly accurate. A limiter for this scheme is fully described that never decreases the polynomial degree, except at the location of extrema. We assess the use of high-order explicit and implicit (i.e., compact) estimates for the edge values and slopes needed to build the piecewise polynomials in both piecewise parabolic method (PPM) and PQM. It is shown that all limited PQM schemes perform significantly better than limited PPM schemes and that PQM schemes are much more cost-effective.