Numerical solutions of 2D Navier-Stokes equations based on generalized harmonic polynomial cell method with non-uniform grid

It is essential for a Navier-Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present numerical solutions of the 2D Navier-Stokes equations using the fourth-order generalized harmonic polynomial cell (GHPC) method as the Poisson equation solver. Particular focus is on the local and global accuracy of the GHPC method on non-uniform grids. Our study reveals that the GHPC method enables use of more stretched grids than the original HPC method. Compared with a second-order central finite difference method (FDM), global accuracy analysis also demonstrates the advantage of applying the GHPC method on stretched non-uniform grids. An immersed boundary method is used to deal with general geometries involving the fluid-structure-interaction problems. The Taylor-Green vortex and flow around a smooth circular cylinder and square are studied for the purpose of verification and validation. Good agreement with reference results in the literature confirms the accuracy and efficiency of the new 2D Navier-Stokes equation solver based on the present immersed-boundary GHPC method utilizing non-uniform grids. The present Navier-Stokes equations solver uses second-order FDM for the discretization of the diffusion and advection terms, which may be replaced by other higher-order schemes to further improve the accuracy.

CARLEMAN'S FORMULA OF A SOLUTIONS OF THE POISSON EQUATION IN BOUNDED DOMAIN

We suggest an explicit continuation formula for a solution to the Cauchy problem for the Poisson equation in a domain from its values and values of its normal derivative on a part of the boundary. We construct the continuation formula of this problem based on the Carleman--Yarmuhamedov function method.

Extraction of Human Motion Information from Digital Video Based on 3D Poisson Equation

Based on the 3D Poisson equation, this paper extracts the features of the digital video human body action sequence. By solving the Poisson equation on the silhouette sequence, the time and space features, time and space structure features, shape features, and orientation features can be obtained. First, we use the silhouette structure features in three-dimensional space-time and the orientation features of the silhouette in three-dimensional space-time to represent the local features of the silhouette sequence and use the 3D Zernike moment feature to represent the overall features of the silhouette sequence. Secondly, we combine the Bayesian classifier and AdaBoost classifier to learn and classify the features of human action sequences, conduct experiments on the Weizmann video database, and conduct multiple experiments using the method of classifying samples and selecting partial combinations for training. Then, using the recognition algorithm of motion capture, after the above process, the three-dimensional model is obtained and matched with the model in the three-dimensional model database, the sequence with the smallest distance is calculated, and the corresponding skeleton is outputted as the results of action capture. During the experiment, the human motion tracking method based on the university matching kernel (EMK) image kernel descriptor was used; that is, the scale invariant operator was used to count the characteristics of multiple training images, and finally, the high-dimensional feature space was mapped into the low-dimensional to obtain the feature space approximating the Gaussian kernel. Based on the above analysis, the main user has prior knowledge of the network environment. The experimental results show that the method in this paper can effectively extract the characteristics of human body movements and has a good classification effect for bending, one-foot jumping, vertical jumping, waving, and other movements. Due to the linear separability of the data in the kernel space, fast linear interpolation regression is performed on the features in the feature space, which significantly improves the robustness and accuracy of the estimation of the human motion pose in the image sequence.

The Prelimit Generator Comparison Approach of Stein’s Method

This paper uses the generator comparison approach of Stein’s method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. The “standard” generator comparison approach starts with the Poisson equation for the diffusion, and the main technical difficulty is to obtain bounds on the derivatives of the solution to the Poisson equation, also known as Stein factor bounds. In this paper we propose starting with the Poisson equation of the Markov chain; we term this the prelimit approach. Although one still needs Stein factor bounds, they now correspond to finite differences of the Markov chain Poisson equation solution rather than the derivatives of the solution to the diffusion Poisson equation. In certain cases, the former are easier to obtain. We use the [Formula: see text] model as a simple working example to illustrate our approach.

Imperfect Fluid Generalized Robertson Walker Spacetime Admitting Ricci-Yamabe Metric

In the present paper, we investigate the nature of Ricci-Yamabe soliton on an imperfect fluid generalized Robertson-Walker spacetime with a torse-forming vector field ξ . Furthermore, if the potential vector field ξ of the Ricci-Yamabe soliton is of the gradient type, the Laplace-Poisson equation is derived. Also, we explore the harmonic aspects of η -Ricci-Yamabe soliton on an imperfect fluid GRW spacetime with a harmonic potential function ψ . Finally, we examine necessary and sufficient conditions for a 1 -form η , which is the g -dual of the vector field ξ on imperfect fluid GRW spacetime to be a solution of the Schrödinger-Ricci equation.

PENYELESAIAN PERSAMAAN POISSON MENGGUNAKAN METODE HOMOTOPI PERTUBASI

In this paper, we discuss the solution of the Poisson equation with some initial condition. We use the homotopy pertubation method to get the solution.. The homotopy pertubation method is a combination of the homotopy method and the pertubation method. The solution of the equation is assumed to be in the form of a power series. The result is by using the homotopy pertubation method for the diffution equation, the solution is the same with the exact solution.