Numerical Effect

Abstract

This chapter discusses the numerical effects, including numerical dissipation, dispersion, and oscillation effects, which are the errors in the process of discretizing continuous media into a numerical system. To demonstrate the psychical dissipation and dispersion, three model equations are chosen as examples to illustrate the essence of physical dissipation and dispersion phenomena and their impact on wave amplitude and phase velocity. Then we use the fully implicit scheme of the wave equation to derive the expressions of numerical dissipation and dispersion coefficients. The amplitude attenuation and phase velocity change caused by numerical errors are explained. And at the end of this chapter, analysis of numerical oscillations in the short-wave component of solution is implemented to display the influencing factors of numerical oscillation effect.