Tidally heated compressible mantle convection in planets and moons

Tidal dissipation associated with the gravitational torque interactions between a satellite and its planet can dramatically affect not only their orbital and respective spin dynamics, but also their internal heat budgets. A complete description of the thermal evolution of planets and moons interiors thus requires to consistently include tidal dissipation in the computation of their internal dynamics. We have developed a new tool, CHEOPS-2D (Coupling Heat transfer and Evolution of the Orbit of Planets and of their Satellites in 2-Dimensional geometry). The conservation equations for the mantle are considered under the anelastic approximation in 2D-Cartesian, cylindrical and spherical annulus (Hernlund and Tackley, PEPI, 2008) geometry. They are discretized using finite-volumes on a staggered mesh. The momentum equation is treated by a multigrid solver (SIMPLER smoother). An explicit scheme is used for the energy balance, with a centered, second-order discretization for diffusion and a high-resolution method (Superbee slope limiter) for advection. The code enables to handle large viscosity gradients. The tidal dissipation contribution is included using the radial functions approach for a viscoelastic body. It corresponds to a heterogeneous internal heating term (but of external origin) in the energy equation. We will first compare our results in 2D-spherical annulus geometry for Earth-like planets with those of Běhounková et al. (JGR-Planets, in press), who used a fully 3D-spherical method under the Boussinesq approximation for the internal dynamics, and an incompressible Maxwell rheology for the tidal dissipation. We will then present the influence of the anelastic approximation and compressible viscoelastic rheology on tidal heating patterns.