Time Integration

Explicit time integration based on Newmark method is conditionally stable. The Courant condition also takes into account the flow of material through the elements gives the stability condition as:(1)
Δ t S f * Δ l c + v w
v w = 1 N i = 1 3 l = 1 N ( v i l w i l ) 2
N MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaaaa@36C9@
Number of nodes for considered elements

The scale factor should be reduced to 0.7 and 0.5 for multi-physics laws.