1,613 research outputs found
Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-Order PDEs
Very singular self-similar solutions of semilinear odd-order PDEs are studied
on the basis of a Hermitian-type spectral theory for linear rescaled odd-order
operators.Comment: 49 pages, 12 Figure
A first-order Green's function approach to supersonic oscillatory flow: A mixed analytic and numeric treatment
A frequency domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. In this range the effects of the nonlinear terms in the unsteady supersonic compressible velocity potential equation are negligible and therefore these terms will be omitted. The Green's function method is employed in order to convert the potential flow differential equation into an integral one. This integral equation is then discretized, through standard finite element technique, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration (e.g., finite-thickness wing, wing-body-tail) is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. The long range goal is to develop a comprehensive theory for unsteady supersonic potential aerodynamic which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range
A first-order time-domain Green's function approach to supersonic unsteady flow
A time-domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. The Green's function method is employed in order to convert the potential-flow differential equation into an integral one. This integral equation is then discretized, in space through standard finite-element technique, and in time through finite-difference, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. Consistent with the spatial linear (first-order) finite-element approximations, the potential and co-normalwash are assumed to vary linearly in time. The long range goal of our research is to develop a comprehensive theory for unsteady supersonic potential aerodynamics which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range
Convergence analysis of a multigrid algorithm for the acoustic single layer equation
We present and analyze a multigrid algorithm for the acoustic single layer
equation in two dimensions. The boundary element formulation of the equation is
based on piecewise constant test functions and we make use of a weak inner
product in the multigrid scheme as proposed in \cite{BLP94}. A full error
analysis of the algorithm is presented. We also conduct a numerical study of
the effect of the weak inner product on the oscillatory behavior of the
eigenfunctions for the Laplace single layer operator
On the cosmological singularity
The long story of the oscillatory approach to the initial cosmological
singularity and its more recent incarnation in multidimensional universe models
is told.Comment: The invited paper for Proceedings of the XIII Marcel Grossmann
Meeting (Stockholm, 2012) by reason of the Marcel Grossmann Award to V.A.
Belinski and I.M. Khalatniko
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