Journal of Scientific Computing
Journal of Computational Physics
Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes
SIAM Journal on Numerical Analysis
The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids
Journal of Computational Physics
Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations
Journal of Computational Physics
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations
Journal of Computational Physics
Nonlinear operator integration factor splitting for the shallow water equations
Applied Numerical Mathematics
Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Accurate interface-tracking for arbitrary Lagrangian-Eulerian schemes
Journal of Computational Physics
SIAM Journal on Scientific Computing
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Hybrid Eulerian-Lagrangian semi-implicit time-integrators (HELSI) are presented which use the standard semi-implicit formulation as their starting point. The advantage of such an approach is that existing models which employ Eulerian semi-implicit time-integrators can easily be augmented to use the HELSI approach, that is, provided that either: a series of advection problems can be solved efficiently as in the operator-integration-factor splitting (OIFS) method or that the grid and underlying numerics allow the construction of efficient search and interpolation stencils typically required of semi-Lagrangian methods. Once the advection problem is solved the approach then follows the standard semi-implicit approach. An important caveat of this approach is that the semi-implicit time-integrator must be constructed around the implicit backward difference formulas.