Development of a Nonlinear k-ε Model Incorporating Strain and Rotation Parameters for Prediction of Complex Turbulent Flows

The standard k-ε model has the deficiency of predicting swirling and vortical flows due to its isotropic assumption of eddy viscosity. In this study, a second-order nonlinear k-ε model is developed incorporating some new functions for the model coefficients to explore the models applicability to complex turbulent flows. Considering the realizability principle, the coefficient of eddy viscosity (cμ) is derived as a function of strain and rotation parameters. The coefficients of nonlinear quadratic term are estimated considering the anisotropy of turbulence in a simple shear layer. Analytical solutions for the fundamental properties of swirl jet are derived based on the nonlinear k-ε model, and the values of model constants are determined by tuning their values for the best-fitted comparison with the experiments. The model performance is examined for two test cases: (i) for an ideal vortex (Stuart vortex), the basic equations are solved numerically to predict the turbulent structures at the vortex center and the (ii) unsteady 3D simulation is carried out to calculate the flow field of a compound channel. It is observed that the proposed nonlinear k-ε model can successfully predict the turbulent structures at vortex center, while the standard k-ε model fails. The model is found to be capable of accounting the effect of transverse momentum transfer in the compound channel through generating the horizontal vortices at the interface.

Weighted Pluricomplex Energy II

We continue our study of the complex Monge-Ampère operator on the weighted pluricomplex energy classes. We give more characterizations of the range of the classes Eχ by the complex Monge-Ampère operator. In particular, we prove that a nonnegative Borel measure μ is the Monge-Ampère of a unique function φ∈Eχ if and only if χ(Eχ)⊂L1(dμ). Then we show that if μ=(ddcφ)n for some φ∈Eχ then μ=(ddcu)n for some φ∈Eχ, where f is given boundary data. If moreover the nonnegative Borel measure μ is suitably dominated by the Monge-Ampère capacity, we establish a priori estimates on the capacity of sublevel sets of the solutions. As a consequence, we give a priori bounds of the solution of the Dirichlet problem in the case when the measure has a density in some Orlicz space.

Direct and Inverse Scattering Problems for Domains with Multiple Corners

We proposed numerical methods for solving the direct and inverse scattering problems for domains with multiple corners. Both the near field and far field cases are considered. For the forward problem, the challenges of logarithmic singularity from Green’s functions and corner singularity are both taken care of. For the inverse problem, an efficient and robust direct imaging method is proposed. Multiple frequency data are combined to capture details while not losing robustness.

Existence of Solutions for a Class of Quasilinear Parabolic Equations with Superlinear Nonlinearities

Working in a weighted Sobolev space, this paper is devoted to the study of the boundary value problem for the quasilinear parabolic equations with superlinear growth conditions in a domain of RN. Some conditions which guarantee the solvability of the problem are given.

A New Method for Inextensible Flows of Timelike Curves in Minkowski Space-Time E14

We construct a new method for inextensible flows of timelike curves in Minkowski space-time E14. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a timelike curve in Minkowski space-time E14.

Conservation Laws for a Degasperis Procesi Equation and a Coupled Variable-Coefficient Modified Korteweg-de Vries System in a Two-Layer Fluid Model via the Multiplier Approach

We employ the multiplier approach (variational derivative method) to derive the conservation laws for the Degasperis Procesi equation and a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model. Firstly, the multipliers are computed and then conserved vectors are obtained for each multiplier.

Improvement of the Modified Decomposition Method for Handling Third-Order Singular Nonlinear Partial Differential Equations with Applications in Physics

The modified decomposition method (MDM) is improved by introducing new inverse differential operators to adapt the MDM for handling third-order singular nonlinear partial differential equations (PDEs) arising in physics and mechanics. A few case-study singular nonlinear initial-value problems (IVPs) of third-order PDEs are presented and solved by the improved modified decomposition method (IMDM). The solutions are compared with the existing exact analytical solutions. The comparisons show that the IMDM is effectively capable of obtaining the exact solutions of the third-order singular nonlinear IVPs.

MHD Equations with Regularity in One Direction

We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, ∂3u∈Lp0, T;LqR3, with 2/p + 3/q = γ ∈ [1,3/2), 3/γ ≤ q ≤ 1/(γ - 1), then the solution is in fact smooth. This improves previous results greatly.

Spectral Bounds for Polydiagonal Jacobi Matrix Operators

The research on spectral inequalities for discrete Schrödinger operators has proved fruitful in the last decade. Indeed, several authors analysed the operator’s canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we consider a generalisation of this relation with regard to connecting higher order Schrödinger-type operators with symmetric matrix operators with arbitrarily many nonzero diagonals above and below the main diagonal. We thus obtain spectral bounds for such matrices, similar in nature to the Lieb-Thirring inequalities.

On Construction of Solutions of Evolutionary Nonlinear Schrödinger Equation

In this work we present an application of a theory of vessels to a solution of the evolutionary nonlinear Schrödinger (NLS) equation. The classes of functions for which the initial value problem is solvable rely on the existence of an analogue of the inverse scattering theory for the usual NLS equation. This approach is similar to the classical approach of Zakharov-Shabath for solving evolutionary NLS equation but has an advantage of simpler formulas and new techniques and notions to understand the solutions.