Acoustic eigenmodes are often used to passively infer physical properties of the interiors of rotating planets and stars. Acoustic wave imaging has been also introduced in fluid dynamics. The experimental technique consists in observing and analysing the splitting in frequency of the acoustic modes, by solving an inverse problem. For instance, the presence of an (unknown) rotational profile disturbs the acoustic spectrum. Moreover, a topographic splitting is often superimposed on the rotational splitting. Indeed, rotating celestial objects are rather ellipsoidal than spherical at the leading order, as well as laboratory experiments which are weakly non-spherical (due to mechanical deformations). Rotation and topography should be taken into account simultaneously, but the acoustic problem does not admit exact solutions in the presence of rotation. Fully numerical solutions are often computed. However, they cannot be easily combined with inversion schemes to yield robust results. Hence, the usual approach is to consider small perturbations to non-rotating solutions. As an alternative, we present a new description of the compressible modes, relying on the method of weighted residuals. Here, we present a new spectral method to describe potential flows in triaxial ellipsoids. It relies on an explicit Galerkin expansion, made of global polynomials expressed in Cartesian coordinates. We illustrate this method by considering the canonical situation of diffusionless acoustic modes in an homogeneous, compressible and homentropic fluid ellipsoid at rest. The pressure satisfies a Dirichlet condition (sound soft boundary). We validate our results against fully numerical simulations performed with the commercial software comsol, showing a perfect quantitative agreement. This new method will be extended to include additional effects and alternative boundary conditions.