This paper presents robust discontinuous Galerkin methods for the incompressible Navier-Stokes equations on moving meshes. High-order accurate arbitrary Lagrangian-Eulerian formulations are proposed in a unified framework both monolithic as well projection or splitting-type solvers. The is flexible, allows implicit and explicit of convective term, adaptive time-stepping. with ALE transport term...

This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for shallow water equations under arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The WENO reconstruction is adopted on moving meshes, which distinguishes smooth, non-smooth, and transition stencils by a simple smoothness detector. To maintain positivi...

In this work we present a high-accurate discretization to solve the compressible Navier-Stokes equations using an Arbitrary Lagrangian-Eulerian meshless method (SPH-MLS), which can be seen as general formulation that includes some well-known meshfree methods particular case. The is based on use of Moving Least Squares (MLS) approximants weight functions Galerkin and accurate discretize convecti...

InN = 1 supersymmetric theories, quasi Nambu-Goldstone (QNG) bosons appear in addition to ordinary Nambu-Goldstone (NG) bosons when the global symmetry G breaks down spontaneously. We investigate two-body scattering amplitudes of these bosons in the low-energy effective Lagrangian formalism. They are expressed by the curvature of Kähler manifold. The scattering amplitudes of QNG bosons are show...

We extend Routh’s reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we analyse the restriction of the Euler-Lagrange field to a level set of momentum in velocity phase space. We present a new method of analysis based on the use ...

Covariantly we reformulate the description of a spinning particle in terms of the Poincaré group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the Lagrangian. Furthermore, in this covariant reformulation, the Lorentz element is to be considered to evolve the momentum or spin component from an arbitrary fixed frame an...

Energy-decreasing continuum flows of geometric order parameters are considered. The dynamics of pattern formation for an arbitrary geometric quantity is derived using a generalization of Darcy’s law based on the geometric nature of the order parameter. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanic...

We study the dynamical equations of nonlinear inductor-capacitor circuits. We present a novel Lagrangian description of the dynamics and provide a variational interpretation, which is based on the maximum principle of optimal control theory. This gives rise to an alternative method for deriving the dynamic equations. We show how this generalized Lagrangian description is related to generalized ...