A novel numerical method named the unified immersed boundary-lattice Boltzmann flux solver (UIB-LBFS) for simulating incompressible flows past homogeneous porous bodies is proposed in this paper. A diffuse layer through which the porosity is smoothly changed is introduced. As a consequence, the governing equations in the porous domain and the pure-fluid domain can be unified. The solutions to each domain can be smoothly transitioned from one to the other through the diffuse layer around the domain interface. A fractional-step technique is employed to split the computational procedure into the predictor step and the corrector step, respectively. In the predictor step, an intermediate flow field is first predicted without considering the domain interface by the unified lattice Boltzmann flux solver. Then, the physical conditions at the fluid–porous interface are implemented through the immersed boundary method to correct the flow field in the corrector step. All the flow quantities are evaluated at the cell centers, while the viscous and the inviscid numerical fluxes are locally reconstructed at each cell interface simultaneously. Numerical validations are carried out, and excellent agreements between the present and published results are achieved. The accuracy and the reliability of the UIB-LBFS are thus proven.

In this paper, the integral methods in general use are divided into two types in terms of their different ways to in order to deal with the temperature integral p(x): for Type A the function h(x)=p(x)x2ex is regarded as constant vs. x, while for Type B h(x) varies vs. x and  ln[p(x)] is assumed to have the approximation form of ln[p(x)]=alnx+bx+c  (the coefficients a, b, and c are constant). The errors of kinetic parameters calculated by these two types of methods are derived as functions of x and analyzed theoretically. It is found that Type A methods have the common errors of activation energy, while the Coats-Redfern method can lead to more accurate value of frequency factor than others. The accuracy of frequency factor can be further enhanced by adjusting the expression of the Coats-Redfern approximation. Although using quite simple approximation of the temperature integral, the Coats-Redfern method has the best performance among Type A methods, implying that usage of a sophisticated approximation may be unnecessary in kinetic analysis. For Type B, the revised MKN method has a lower error in activation energy and an acceptable error in frequency factor, and thus it can be reliably used. Comparatively, the Doyle method has higher error of activation energy and great error of the frequency factor, and thus it is not recommended to be adopted in kinetic analysis.