Implementation of a high-order compact finite-difference lattice Boltzmann method in generalized curvilinear coordinates

The principle of velocity decomposition is used to combine field discretization and boundary-element techniques to solve for steady, viscous, external flows around bodies. The decomposition modifies the Navier---Stokes boundary-value problem and produces a Laplace problem for a viscous potential, and a new Navier---Stokes sub-problem that can be solved on the portion of the domain where the total velocity has rotation. The key development in the decomposition is the formulation for the boundary condition on the viscous potential that couples the two components of velocity. An iterative numerical scheme is described to solve the decomposed problem. Results are shown for the steady laminar flow over a sectional airfoil, a circular cylinder with separation, and the turbulent flow around a slender body-of-revolution. The results show the viscous potential is obtainable even for massively separated flows, and the field discretization must only encompass the vortical region of the total velocity.

A velocity-decomposition formulation for the incompressible Navier---Stokes equations

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A Velocity Decomposition Method for Efficient Numerical Computation of Steady External Flows.

This thesis introduces a new parameterization technique based on the Class-Shape-Transformation (CST) method. The new technique consists of an extension to the CST method in the form of a refinement function based on B-splines. This Class-Shape-Refinement-Transformation (CSRT) method has the same advantages as the original CST method, while also allowing for local deformations in a shape. A number of test cases were performed using two different design frameworks with low and high fidelity. The low fidelity framework was based on a commercial panel method code and coupled to various optimization algorithms. The high fidelity framework used an in-house Euler code and employed adjoint optimization.

Shape Parameterization in Aircraft Design: A Novel Method, Based on B-Splines

Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

Viscous/Inviscid Interaction procedures consist usually of coupling potential flow and boundary layer calculations. In this study, the interaction is modeled using Helmholtz-type velocity decomposition where the gradient of the potential is augmented with a correction accounting for the vorticity effects in the viscous layers. Different ways to calculate the rotational components are discussed and methods to systematically improve the model are studied. Numerical results are compared with standard Navier-Stokes calculations to justify the present approach.

Improved Numerical Simulations of Incompressible Flows Based on Viscous/Inviscid Interaction Procedures

A stagewise theoretical substantiation of the renovation vibrowave method of influencing the near-wellbore zone of reservoir for restoring well productivity is presented. The area of treatment by the proposed method covers the reservoir with a heterogeneous permeability with fractures formed by fracking. In this method a decrease in concentration of colmatants occurs due to a change in direction of contaminants migration. Under the influence of pressure pulses, they move deep into the reservoir and disperse through the proppant pack. The results of mathematical modelling of the propagation of pressure wave and velocity wave and the calculations of particles entrainment in wave motion are presented.

A. Shatalov

Papers

Improved Numerical Simulations of Incompressible Flows Based on Viscous/Inviscid Interaction Procedures

Improved Numerical Simulations of Incompressible Flows Based on Viscous/Inviscid Interaction Procedures

Renovation method of restoring well productivity using wavefields