Toward Absolutely Stable Numerical Scheme

ISBN-13: 9783659686283 / Angielski / Miękka / 2015 / 296 str.

Sakai Katsuhiro

Opis

As a milestone for compatibility between the numerical stability and accuracy in numerical analysis for advection-diffusion equations, this book presents third-order self-adaptive polynomial schemes to guarantee the nonnegativity condition for any computational conditions in both nonconservative form and conservative form by no means of flux limiters. As an application to advection equations, the present scheme would be suggestive of a necessary and sufficient artificial viscosity to be locally added with the third-order accuracy anywhere. Further this book presents an analytical solution of linear and nonlinear advection-diffusion equations, especially presented a new analytical solution of three-dimensional nonlinear advection-diffusion equations. Based on those analytical solutions, this book presents locally exact noble schemes with nonnegativity properties. These schemes are characterized by a self-consistent nature with an analytical solution of advection-diffusion equations, resulting in guaranteeing the nonnegativity condition anywhere in any steep gradient field. Thus the present locally exact schemes would be a candidate toward "absolutely stable numerical scheme".

O autorze

Katsuhiro Sakai, Emeritus Prof. of Saitama Institute of Technology, has studied theoretical physics and nuclear engineering, and obtained Doctor Engineering degree in Nuclear Engineering in 1979. Fields of study are Numerical Analysis Theory and Computational Fluid Dynamics. Main subject is "compatibility between numerical stability and accuracy".