A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in past that this coupled PDEs fact an encoding entire Kadomtsev-Petviashvili (KP) hierarchy terms so-called Miwa variables. Thus, providing description multidimensionally consistent amounts to new 3-form continuous KP system. matrix ...

A geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements, and is suitable for both solid and liquid membranes. The curvilinear coordinate system is used to describe both the theory and the finite element equations of the membrane. In the latter case this avoids the use of local cartesian coordinates at the element level. C...

Keywords: BiGlobal Stability Airfoil Ellipse Separation Conformal mapping A methodology based on spectral collocation numerical methods for global flow stability analysis of incompressible external flows is presented. A potential shortcoming of spectral methods, namely the handling of the complex geometries encountered in global stability analysis, has been dealt with successfully in past works...

A mathematical scheme is proposed here to model a damaged mechanical configuration for laminated and sandwich structures. In particular, two kinds of functions defined in the reference domain of plates and shells are introduced to weaken their mechanical properties in terms of engineering constants: a two-dimensional Gaussian function and an ellipse shaped function. By varying the geometric par...

The study of the Andaman Sea can be studied by using the oceanic model; therefore the grid covering the study area should be generated. This research aims to generate grid covering the Andaman Sea, situated between longitudes 90◦E to 101◦E and latitudes 1◦N to 18◦N . A horizontal grid is an orthogonal curvilinear with 87 × 217 grid points. The methods used in this study are cubic spline and bil...

On unique parametrization of the linear group GL(4.C) and its subgroups by using the Dirac matrix algebra basis A unifying overview of the ways to parameterize the linear group GL(4.C) and its subgroups is given. As parameters for this group there are taken 16 coefficients G = G(A, B, A k , B k , F kl) in resolving matrix G ∈ GL(4.C) in terms of 16 basic elements of the Dirac matrix algebra. Al...

Provably stable flux reconstruction (FR) schemes are derived for partial differential equations cast in curvilinear coordinates. Specifically, energy (ESFR) considered as they allow design flexibility well stability proofs the linear advection problem on affine elements. Additionally, split forms examined enable development of proofs. The first critical step proves, that coordinates, discontinu...

Abstract Numerical models for calculating bottom morphology are increasingly popular because of their long-term forecasting capabilities as well ability to identify causes. However, the simulation morphology, in addition natural factors, is also governed by economic activities, especially sand mining. In this paper, we propose development numerical model curvilinear coordinates combined with a ...

We study the non–linear dynamics of self–gravitating irrotational dust in a general relativistic framework, using synchronous and comoving (i.e. Lagrangian) coordinates. All the equations are written in terms of a single tensor variable, the metric tensor of the spatial sections orthogonal to the fluid flow. This treatment allows an unambiguous expansion in inverse (even) powers of the speed of...