Kazuya Nojima

SUPG finite element method for adiabatic flows

The purpose of this paper is to present the SUPG finite element method for adiabatic flows and to compare the results with those obtained via various computational methods. The incompressibility assumption is often used to solve transient viscous flows. On the other hand, compressible flow analyses are also popular because natural flows include compressibility even if it is a negligible amount. It is well known that incompressibility is a limit state of compressibility. To solve compressible flows, three kinds of governing equations are needed: the conservation of mass, momentum, and energy, in which density, velocity, and internal energy are independent variables. If we assume that there is no heat transfer in or out of a system, the energy equation can be eliminated from the governing equations. Density and velocity can be considered independent variables. These kinds of flows are referred to as adiabatic flows in this paper. The SUPG formulation is one of the most widely used methods in the finite element analyses of fluid flows. In this paper, the SUPG method for adiabatic flows is presented. The polytropic law is introduced for the equation of state. Moreover, the computational results obtained by four models of fluid flows are compared: adiabatic flows, compressible flows, constant acoustic velocity flows, and incompressible flows. Verifications are carried out using a lid-driven cavity flow. Boundary effects are estimated using a wide computational domain. Drag forces are compared with those computed using incompressible flows. The pressure coefficients over a surface of a circular cylinder located in fluid flows computed by the present method show good correspondence with the experimental measurement. On the other hand, significant discrepancies are observed between the pressure coefficients computed assuming constant density and the experimental results.

Three‐Dimensional Shape Identification of a Body Located in Fluid Flow

This study presents a numerical method of shape identification of the body located in viscous flow. The purpose of this study is to determine the shape of body located in a viscous flow, where the applied fluid force is minimized. In this study, the formulation to obtain the optimal shape is based on the optimal control theory. The finite element method is used for the calculation of fluid flow. In this study an optimal control is treated as fluid force minimization. Therefore, fluid forces are used in the performance function directly. The shape identification must be carried out satisfying the state equation. Therefore, the minimization with constraint condition is required. In this study, the Lagrange multipliers are introduced for the constraint minimization problem. In this study, an optimized shape of a body is obtained by computation. In the optimizing computation, a sphere is set into the computational domain as initial shape.

Second-order adjoint equation method for parameter identification of rock based on blast waves in tunnel excavation

The objective of this study is to present a method for identifying the elastic moduli of ground rock via the first- and second-order adjoint methods using blast vibration measurements during tunnel excavation. For identifying these parameters, the magnitudes of the blast force should be identified beforehand. Parameter identification is a minimization problem of the square sum of the discrepancy between the computed and observed velocities. The magnitudes of the three components of borehole pressure are assumed to be independent in each direction. The propagation of an elastic wave is assumed because the amplitude of such a wave is infinitesimal. The three-dimensional finite element method and the linear acceleration method are used effectively. The extended performance function can be expanded into a series of small constants to derive the necessary condition of minimization. The adjoint equation and the dynamic equation of motion can be used to obtain the gradient and the Hessian product of the extended performance function with respect to the parameters. The weighted gradient method and Broyden–Flecher–Goldfarb–Shanno method are successfully employed for the minimization. By applying the present identification technique at the Ohyorogi tunnel site, the fact that the computed and observed velocities are well in agreement is verified. The present method can be shown to be useful for tunnel excavation.