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

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...

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 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...

In this paper we will show that contouring performance can be viewed as a regulation problem in a curvilinear task coordinate frame that is attached to the desired contour. By transforming the machine tool feed drive dynamics to this task coordinate frame, an adaptive robust control (ARC) law is derived to improve the contouring performance under system parameter variation and bounded disturban...

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...