  We present an energy conserving space discretisation based on a Poisson
bracket that can be used to derive the dry compressible Euler as well as
thermal shallow water equations. It is formulated using the compatible finite
element method, and extends the incorporation of upwinding for the shallow
water equations as described in Wimmer, Cotter, and Bauer (2019). While the
former is restricted to DG upwinding, an energy conserving SUPG scheme for the
(partially) continuous Galerkin thermal field space is newly introduced here.
The energy conserving property is validated by coupling the Poisson bracket
based spatial discretisation to an energy conserving time discretisation.
Further, the discretisation is demonstrated to lead to an improved temperature
field development with respect to stability when upwinding is included. An
approximately energy conserving full discretisation with a smaller
computational cost is also presented.
