Related papers: Selective decay for the rotating shallow-water equ…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics…
We use the general framework of summation-by-parts operators to construct conservative, energy-stable, and well-balanced semidiscretizations of two different nonlinear systems of dispersive shallow water equations with varying bathymetry:…
Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for…
Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
We develop a rigorous theory for a structure-preserving discretisation of the incompressible Euler and Navier--Stokes equations, based on discrete exterior calculus on prismatic Delaunay--Voronoi meshes over closed Riemannian manifolds. The…
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…
We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their $L^2$ algebraic decay. Some of these inequalities have not been…
We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on…
In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It is based on a suitable…
Modifications of the equations of ideal fluid dynamics with advected quantities are introduced that allow selective decay of either the energy $h$ or the Casimir quantities $C$ in the Lie-Poisson formulation. The dissipated quantity (energy…
We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore,…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…