A. I. Tolstykh
Russian Academy of Sciences
38 Papers
238 Citations
A. I. Tolstykh is an academic researcher from Russian Academy of Sciences. The author has contributed to research in topics: Discretization & Navier–Stokes equations. The author has an hindex of 10, co-authored 33 publications. Previous affiliations of A. I. Tolstykh include Moscow Institute of Physics and Technology.
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Papers
On using radial basis functions in a “finite difference mode” with applications to elasticity problems
A. I. Tolstykh,D. A. Shirobokov +1 more
TL;DR: A way of using RBF as the basis for PDE’s solvers is presented, its essence being constructing approximate formulas for derivatives discretizations based on RBF interpolants with local supports similar to stencils in finite difference methods.
290
On Performance of Methods with Third- and Fifth-Order Compact Upwind Differencing
TL;DR: The difference schemes for fluid dynamics type of equations based on third and fifth-order Compact Upwind Differencing (CUD) are considered in this paper, and the performance of the CUD methods is estimated by investigating mesh convergence of the solutions and comparing with the results of second-order schemes.
58
High-accuracy discretization methods for solid mechanics
TL;DR: Novel high-accuracy computational techniques for solid mechanics problems are presented, including fourth-order and arbitrary-order finite difference methods based on Pade-type differencing formulas and a meshless method which uses radial basis functions in a "finite difference" mode.
28
Fast calculations of screech using highly accurate multioperators-based schemes
A. I. Tolstykh,D.A. Shirobokov +1 more
TL;DR: The seventh- and ninth-order multioperators optimized schemes for the Navier–Stokes equations are tested and applied to the 2D screech problem and the scenario of screech generation was found to conform with the shock leakage theory.
24
Development of arbitrary-order multioperators-based schemes for parallel calculations. 1: Higher-than-fifth-order approximations to convection terms
TL;DR: It is shown that for properly chosen parameters, multioperators preserve the upwind (downwind) properties of the basis operators, that is their positivity (negativity) in appropriate Hilbert spaces of grid functions.
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