Let $k$ be a field, $R$ a $k$-algebra (of finite type if necessary), $B$ an algebra of finite type over ring of the formal Laurent series $R((t))$, which is smooth.

Up to this generality, can one construct a flat model of $B$ over ring of formal power series $R[[t]]$ (i.e. a flat algebra $\tilde{B}$ over $R[[t]]$ such that $\tilde{B}\otimes_{R[[t]]}R((t))=B$)?

If not, what could be the weakest assumption that will allow this?