  A recent result by J. \v{S}aroch and J. \v{S}\v{t}ov\'{\i}\v{c}ek asserts
that there is a unique abelian model structure on the category of left
$R$-modules, for any associative ring $R$ with identity, whose (trivially)
cofibrant and (trivially) fibrant objects are given by the classes of
Gorenstein flat (resp., flat) and cotorsion (resp., Gorenstein cotorsion)
modules. In this paper, we generalise this result to a certain relativisation
of Gorenstein flat modules, which we call Gorenstein $\mathcal{B}$-flat
modules, where $\mathcal{B}$ is a class of right $R$-modules. Using some of the
techniques considered by \v{S}aroch and \v{S}\v{t}ov\'{\i}\v{c}ek, plus some
other arguments coming from model theory, we determine some conditions for
$\mathcal{B}$ so that the class of Gorenstein $\mathcal{B}$-modules is closed
under extensions. This will allow us to show approximation properties
concerning these modules, and also to obtain a relative version of the model
structure described before. Moreover, we also present and prove our results in
the category of complexes of left $R$-modules, study other model structures on
complexes constructed from relative Gorenstein flat modules, and compare these
models via computing their homotopy categories.
