Continuous and Discrete Adjoint Approach Based on Lattice Boltzmann Method in Aerodynamic Optimization Part I:Mathematical Derivation of Adjoint Lattice Boltzmann Equations

The significance of flow optimization utilizing the lattice Boltzmann(LB)method becomes obvious regarding its advantages as a novel flow field solution method compared to the other conventional computational fluid dynamics techniques.These unique characteristics of the LB method form the main idea of its application to optimization problems.In this research,for the first time,both continuous and discrete adjoint equations were extracted based on the LB method using a general procedure with low implementation cost.The proposed approach could be performed similarly for any optimization problem with the corresponding cost function and design variables vector.Moreover,this approach was not limited to flow fields and could be employed for steady as well as unsteady flows.Initially,the continuous and discrete adjoint LB equations and the cost function gradient vector were derived mathematically in detail using the continuous and discrete LB equations in space and time,respectively.Meanwhile,new adjoint concepts in lattice space were introduced.Finally,the analytical evaluation of the adjoint distribution functions and the cost function gradients was carried out.

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales. Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REV and hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2 D or 3 D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.

Linking discrete particle simulation to continuum process modelling for granular matter: Theory and application

Two approaches are widely used to describe particle systems： the continuum approach at macroscopic scale and the discrete approach at particle scale. Each has its own advantages and disadvantages in the modelling of particle systems. It is of paramount significance to develop a theory to overcome the disadvantages of the two approaches. Averaging method to link the discrete to continuum approach is a potential technique to develop such a theory. This paper introduces an averaging method, including the theory and its application to the particle flow in a hopper and the particle-fluid flow in an ironmaking blast furnace.

Adjoint based state estimation of compressible flow in porous media

In this paper,we study the state estimation of compressible single phase flow in compressible porous media.The initial pressure distribution is estimated according to discrete adjoint approach based on the collected well pressure data.The first-order Tykhonov regularization method is used to obtain reasonable estimation.By analyzing the optimality condition of estimation problem,the discrete adjoint state equation and discrete adjoint gradient are derived based on the numerical scheme of the continuous equations.A quasi-Newton numerical optimization method related to adjoint gradient is proposed to solve the estimation problem.The estimation results with different regularization coefficients are compared and analyzed by numerical experiments.The deviation between the estimated pressure obtained without regularization and the real pressure is large.Estimation result with smaller deviation and higher smoothness can be obtained through appropriate regularization coefficient.When the observation error is large,the observed values generated by the estimated pressure fit well with the real pressure.

Comparative Study on Two Methods for Calculating the Gravitational Potential of a Prism

The determination of the gravitational potential of a prism plays an important role in physical geodesy and geophysics. However, there are few literatures that provide accurate approaches for determining the gravitational potential of a prism. Discrete element method can be used to determine the gravitational potential of a prism, and can approximate the true gravitational potential values with sufficient accuracy (the smaller each element is, the more accurate the result is). Although Nagy's approach provided a closed expression, one does not know whether it is valid, due to the fact that this approach has not been confirmed in literatures. In this paper, a study on the comparison of Nagy's approach with discrete element method is presented. The results show that Nagy's formulas for determining the gravitational potential of a prism are valid in the domain both inside and outside the prism.