The water hammer phenomenon is the main problem in long-distance pipeline networks. MOC (Method of characteristics) and finite difference methods lead to severe constraints on mesh Courant number, while volume method second-order Godunov scheme has limited intermittent capture capability. These will produce numerical dissipation, affecting computational efficiency at low numbers. Based lax-Frie...

Discontinuous Galerkin Methods for Friedrichs Systems with Irregular Solutions Max Jensen Doctor of Philosophy Corpus Christi College Michaelmas Term 2004 This work is concerned with the numerical solution of Friedrichs systems by discontinuous Galerkin finite element methods (DGFEMs). Friedrichs systems are boundary value problems with symmetric, positive, linear first-order partial differenti...

We show that a recently introduced Lax pair of the Sawada-Kotera equation is nota new one but is trivially related to the known old Lax pair. Using the so-called trivialcompositions of the old Lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.

Given a pseudomonad $mathcal{T} $ on a $2$-category $mathfrak{B} $, if a right biadjoint $mathfrak{A}tomathfrak{B} $ has a lifting to the pseudoalgebras $mathfrak{A}tomathsf{Ps}textrm{-}mathcal{T}textrm{-}mathsf{Alg} $ then this lifting is also right biadjoint provided that $mathfrak{A} $ has codescent objects. In this paper, we give  general results on lifting of biadjoints. As a consequence, ...

we show that a recently introduced lax pair of the sawada-kotera equation is nota new one but is trivially related to the known old lax pair. using the so-called trivialcompositions of the old lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial lax pairs of kdv and sawada-kotera equations.

We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.

ABSTRACT Non-Newtonian rheology effects, such as pseudoplasticity and viscoplasticity, are understood shear stresses, incorporated to the energy slope term in Shallow-Water Equations (SWE). However, non-Newtonian stresses dependent of rate, whose formulation is a function gradient velocity profile bottom. This study investigated two rate formulations that commonly applied SWE literature: 1) non...

This paper develops the high-order accurate entropy stable (ES) finite difference schemes for shallow water magnetohydrodynamic (SWMHD) equations. They are built on numerical approximation of modified SWMHD equations with Janhunen source term. First, second-order well-balanced semi-discrete conservative (EC) constructed, satisfying identity given convex function and preserving steady states lak...

Seismic waves in earth media usually undergo attenuation, causing energy losses and phase distortions. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation attenuating media, where real imaginary parts function capture dispersion effects amplitude attenuation seismic waves, respectively. Conventionally, such mainly comp...