Yasunori Motoyama

Reliability Analysis of CFD Solution Using Sensitivity Theory

In this study, we present a new numerical method to quantitatively analyze the reliability of numerical models by using the sensitivity theory. If a reference case of typical parameters is once calculated with the method, no additional calculation is required to estimate the results of the other numerical parameters such as more detailed solutions. Furthermore, we can estimate the strict solution from the sensitivity analysis results and can quantitatively evaluate the reliability of the numerical solution by calculating the numerical error.Copyright

Error Estimation of Numerical Solutions of One-dimensional Burgers Equation by Adjoint Sensitivity Analysis Method

In this study, we present a new numerical method to analyze quantitatively the error of numerical solution by using the adjoint sensitivity analysis method and the modified equation approaches. If a reference case of typical parameters is once calculated with the method, no additional calculation is required to estimate the results of the other numerical parameters such as those of more detailed resolution. Furthermore, we can estimate the strict solution from the sensitivity analysis results and can quantitatively evaluate the error of numerical solutions based on only the numerical procedures.

Sensitivity analysis of numerical results of one- and two-dimensional advection-diffusion problems

Numerical simulation has been playing an increasingly important role in the fields of science and engineering. However, every numerical result contains errors such as modeling, truncation, and computing errors, and the magnitude of the errors that are quantitatively contained in the results is unknown. This situation causes a large design margin in designing by analyses and prevents further cost reduction by optimizing design. To overcome this situation, we developed a new method to numerically analyze the quantitative error of a numerical solution by using the sensitivity analysis method and modified equation approach. If a reference case of typical parameters is calculated once by this method, then no additional calculation is required to estimate the results of other numerical parameters such as those of parameters with higher resolutions. Furthermore, we can predict the exact solution from the sensitivity analysis results and can quantitatively evaluate the error of numerical solutions. Since the method incorporates the features of the conventional sensitivity analysis method, it can evaluate the effect of the modeling error as well as the truncation error. In this study, we confirm the effectiveness of the method through some numerical benchmark problems of one- and two-dimensional advection-diffusion problems.