The very large viscosity of solid planets, together with their large dimensions, makes their inertia negligible (infinite Prandtl number) while also giving them very high Rayleigh numbers (10$^7$-10$^{10}$). For planets with liquid layers (e.g. magma oceans, metallic cores or deep oceans), the Rayleigh and Prandtl number ranges are enormous. The radial density of these planets increases with depth due to compressibility, leading to impacts on their convective dynamics. To account for these effects, including the presence of a depth variation of the thermal expansivity, a quasi-adiabatic temperature profile and entropy sources due to dissipation, the compressibility is expressed through a dissipation number, $\mathcal D$, proportional to the planet's radius and gravity. Compressibility effects are moderate in Earth's mantle ($\mathcal D\approx 0.5$), but in large rocky or liquid exoplanets (super-Earths), the dissipation number can become very large ($\mathcal D\approx 20$). In this presentation, we will explore the properties of compressible convection when the dissipation number is significant and the Prandtl number is infinite. Unlike the prototypical case of perfect gas convection, the adiabatic temperature gradient in condensed materials is nonlinear, which asymmetrises the top and bottom boundary layers, as well as the dynamics of hot and cold plumes. A much larger adiabatic heat flow is carried out in the cold shallow layers that can impede convection near the surface and imposes a top boundary layer controlled by compressibility. We will present numerical simulations of convection in 2D Cartesian geometry performed using the exact equations of mechanics, neglecting inertia (infinite Prandtl number), and examine their consequences for super-Earth dynamics. We will also discuss the differences between exact simulations and simulations using approximated anelastic formalism. We will demonstrate how these differ from the first order simulations often used in the solid Earth community, where parameters are varied within an overwise Boussinesq formalism to which an adiabatic gradient is added a posteriori.