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Discontinuous Galerkin methods for short pulse type equations via hodograph transformations

Qian Zhang, Yinhua Xia
2019 Journal of Computational Physics  
In the present paper, we consider the discontinuous Galerkin (DG) methods for solving short pulse (SP) type equations.  ...  Through hodograph transformations, these nonclassical solutions can be profiled as the smooth solutions of the coupled dispersionless (CD) system or the sine-Gordon equation.  ...  type equations can be also adopted to solve these generalized short pulse type equations via hodograph transformations.  ... 
doi:10.1016/j.jcp.2019.108928 fatcat:seebi5oqijhgleqawmyjjcyjwu

Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation [article]

Qian Zhang, Yinhua Xia
2019 arXiv   pre-print
In this paper, we develop discontinuous Galerkin (DG) methods for the Ostrovsky-Vakhnenko (OV) equation, which yields the shock solutions and singular soliton solutions, such as peakon, cuspon and loop  ...  For some singular solutions, including cuspon and loop soliton solutions, the hodograph transformation is adopted to transform the OV equation or the generalized OV system to the coupled dispersionless  ...  is also applied in [41] for the short pulse equation.  ... 
arXiv:1908.03873v1 fatcat:ra453grz2bgdhmdai3ergdyafq

Analysis and numerical investigation of two dynamic models for liquid chromatography

Shumaila Javeed, Shamsul Qamar, Waqas Ashraf, Gerald Warnecke, Andreas Seidel-Morgenstern
2013 Chemical Engineering Science  
Two numerical schemes, namely the finite volume scheme of Koren and the discontinuous Galerkin finite element method, are applied to numerically approximate the models considered.  ...  The models consist of systems of convection-diffusion-reaction partial differential equations with dominating convective terms coupled via differential or algebraic equations.  ...  The Discontinuous Galerkin finite element method was initially introduced by Reed and Hill [71] for solving neutron transport equations.  ... 
doi:10.1016/j.ces.2012.12.014 fatcat:5ir6oeszxracziabplekmhipxi

Danish activities concerning noise in the environment

Fritz Ingerslev
1982 Journal of the Acoustical Society of America  
Normal detection methods that examine noise emitted by the collapsing cavity can not be used in short-pulse excitation due to the high spectral content of the pulse itself.  ...  Other methods used to analyze the dynamics of structures include the differential equation and energy methods.  ...  The temperature discontinuity divides the tube into two homogeneous regions.  ... 
doi:10.1121/1.2019901 fatcat:kk6boa5no5aitorvgbktvdlxou

A discontinuous Galerkin method for the solution of compressible flows

Cristian Biotto, Joaquim Peiró
2011
This thesis presents a methodology for the numerical solution of one-dimensional (1D) and two-dimensional (2D) compressible flows via a discontinuous Galerkin (DG) formulation.  ...  An artificial diffusion term is implemented to stabilise the solution of the Euler equations in transonic flow with discontinuities.  ...  This is analysed in detail in [67] , where for the discontinuous Galerkin method they define CFL∝ p −2 .  ... 
doi:10.25560/6413 fatcat:fivlalfegvgi7px7iglmtc433y

Simulating unsteady conduit flows with smoothed particle hydrodynamics [article]

Hou, Q (Qingzhi), Mattheij, RMM (Robert = Bob), Tijsseling, AS (Arris)
2012
The hodograph transformation method used in [39, 139] is efficient for two-dimensional and axisymmetric problems [39, 78] .  ...  From the potential flow theory, with the use of conformal mapping or hodograph transformations, an integral-differential equation for the free surface(s) of the jet is formulated.  ...  When the weak form of a PDE is solved using a Galerkin method, direct correction to the function approximation is often used as in the element-free Galerkin (EFG) method [16] , which is one of the most  ... 
doi:10.6100/ir733420 fatcat:3hlvh2rswza4xpzgcdmydxoudu

A geometrically nonlinear approach for the aeroelastic analysis of commercial transport aircraft

Alvaro Cea Esteban, Rafael Palacios Nieto, Engineering And Physical Sciences Research Council, Airbus Industrie
2021
A new approach is proposed that seamlessly integrates with current industrial aeroelastic load analysis methods and aims to bring together the complexity of computational models in the production environment  ...  and secondly, a manipulation of the resulting condensed stiffness and mass matrices, their linear normal modes, and the nodal coordinates provide the nonlinear modal coefficients of the intrinsic beam equations  ...  via an inverse Fourier transform.  ... 
doi:10.25560/89976 fatcat:hmgcojipjbawzfoxg4c44ecas4