Integrability criterion for the Egorov hydrodynamic type systems is presented. The general solution by the generalized hodograph method is found. Examples are given. A description of three orthogonal curvilinear coordinate nets is discussed from the viewpoint of reciprocal transformations. In honour of Sergey Tsarev

Objectives . A finite-difference computational algorithm is proposed for solving a mixed boundary-value problem the Poisson equation given in two-dimensional irregular domains. Methods To solve problem, generalized curvilinear coordinates are used. The physical domain mapped to (unit square) space of coordinates. original written and approximated on uniform grid domain.The obtained results non-...

Vibrational states of the formic acid molecule are converged using GENIUSH-Smolyak approach and potential energy surface taken from [D. Tew W. Mizukami, J. Phys. Chem. A 120, 9815 (2016)]. The quantum nuclear motion is described by $cis$-$trans$ torsional coordinate eight curvilinear normal coordinates defined with respect to an instantaneous reference configuration changing as a function degre...

The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of (n−d) curvilinear coordinates parametrizing the manifold of configurations satisfying the constraints, and to compute the Lagrangian generating the unconstrained dynamics in these (n−d) configuration coordinates. Starting from this...

Through mathematical models, it is possible to turn a problem of the physical domain computational domain. In this context, paper presents two-dimensional mesh generator in generalized coordinates, which uses parametric linear spline method and partial differential equations. The automated able treat real complex domains and, consequently, more realistic problems. However, there possibility tha...

The paper deals with the derivation of entropy production in fluid flow performed a general curvilinear coordinate system. is based on thermodynamics laws as well balances mass, momentum, and energy. A brief description differential geometry used coordinates presented here to define notation.The application this approach then shown evaluation along suction side blade, where calculation was usin...