= Triangular current with capillary retention
{title2=$h=a\max\{0,\min(x-v_Rt,2L+v_At-x)\}$}
For <capillary residual trapping> of an initial triangular current, the <method of characteristics> translates its leading and trailing faces at $v_A=u/\phi$ and $v_R=u/[\phi(1-s)]$. Their intersection has height $a[L-(v_R-v_A)t/2]$. Extinction occurs at $t_*=2L/(v_R-v_A)$ and position $x_*=2L/s$. These formulas require $0<s<1$; at zero residual saturation the triangle translates indefinitely.
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