A method to accurately define arbitrary algorithmic damping character as viscous damping

Undesired oscillations often emerge in numerical solutions, especially in the case of dynamic problems. These are mainly spurious oscillations which must be eliminated or reduced at least to provide accurate results. Numerical methods with damping effect are especially useful to achieve this goal. However, the concrete shape of the damping characteristics has a great impact on the effectiveness. Dissipative numerical methods mostly have a specific damping character with very limited alteration possibility. In this article, a novel numerical method has been introduced where the dissipative effect is exerted via viscous damping. Using the proposed method, a great variety of damping curves can be defined accurately, straight through the determination of the algorithmic damping ratio. The newly developed technique is mainly useful for applications where the shape of the damping characteristics significantly affects the accuracy.

Automated summary

Undesired oscillations often occur in numerical solutions, especially in dynamic problems. Damping effect in numerical methods can eliminate or reduce these spurious oscillations for accurate results. This article introduces a novel numerical method using viscous damping to define a variety of damping curves accurately, particularly suitable for applications where damping characteristics significantly affect accuracy.