In this work, we adopt the equations presented by Mckee (1989).
We adopted the equation (Eq. 1) proposed by Noguchi and Sasatani (2008) to quantify the degree of nonlinearity (DNL) based on the S-H/V spectral ratios.
Accounting for non-equilibrium effects between the constituent fluid phases, i.e. temperature differences between phases, the model calculates the time variation of fluid pressure, temperature and composition inside the vessel adopting the equations of state for non-ideal gas.
As for the calculation of gas viscosity, we adopt the empirical equation proposed by Huanlin (1988); following equations are the procedure.
In this study, we consider the fractal characteristics of the porous GDL as well as its general microstructure, and we adopt the Bosanquet equation to derive effective diffusivity.
To predict the electric fields due to the tsunami wave motion, we adopt the integral equation numerical solution described by Kuvshinov et al. (2002) and Kuvshinov and Olsen (2005).
Soil moisture in a hillslope is simulated using three multi-dimensional hydrologic models: a 3D surface subsurface integrated model and two 2D distributed hydrologic models, MIKE-SHE and WEP, which adopt the Richards equation at different levels of approximation.
We adopt the Euler equations with a fast kinetic solver in the region near thermodynamical equilibrium, while use the Boltzmann-BGK equation in kinetic regions where fluids are far from equilibrium.
In this paper, we adopt the Riccati-equation based algorithm, one of the iterative algorithms, and demonstrate the proposed algorithmic method is applicable to such mechanical systems as fast-sampling is required.
Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.
