Related papers: Group classification of steady two-dimensional bou…
We study the geometry of streamlines and stability properties for steady state solutions of the Euler equations for ideal fluid.
The stochastic motion of a two-dimensional vesicle in linear shear flow is studied at finite temperature. In the limit of small deformations from a circle, Langevin-type equations of motion are derived, which are highly nonlinear due to the…
We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded multiply connected domain. We prove that this problem has a solution in some…
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for…
We propose a general framework to extend Flow Matching to homogeneous spaces, i.e. quotients of Lie groups. Our approach reformulates the problem as a flow matching task on the underlying Lie group by lifting the data distributions. This…
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…
Given a class of differential equations with arbitrary element, the problems of symmetry group, nonclassical symmetry and conservation law classifications are to determine for each member the structure of its Lie symmetry group, conditional…
This paper investigates the nature of the development of vortex shedding for two-dimensional unsteady flow of an incompressible fluid at the rear stagnation point.
In this paper, we discuss the method of obtaining symmetries for second order nonhomogeneous neutral differential equations with variable coefficients. We use Taylor theorem for a function of several variables to obtain a Lie type…
A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is…
We study shear-free spherically symmetric relativistic models with heat flow. Our analysis is based on Lie's theory of extended groups applied to the governing field equations. In particular, we generate a five-parameter family of…
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve an equivalent first-order PDE system of…
The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and…
We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant…
A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the…
We analyze static point-to-set correlations in glass-forming liquids. The generic idea is to freeze the position of a set of particles in an equilibrium configuration and to perform sampling in the presence of this additional constraint.…
In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations with functional derivatives. In order to perform the group analysis and deal with the functional…
We reprove the $\lambda$-Lemma for finite dimensional gradient flows by generalizing the well-known contraction method proof of the local (un)stable manifold theorem. This only relies on the forward Cauchy problem. We obtain a rather…