Scaling laws for internally heated mantle convection This work presents a new method to simulate mantle convection in a 3D spherical shell with fully spatially varying viscosities. The formulation of the governing equations is based on the finite volume (FV) method for fully irregular grids using Voronoi cells. The simulation code is efficiently parallelized for more than 1000 CPUs. A new irregular grid with varying lateral resolution the spiral grid was investigated. The discretization method is second order accurate in space and time. The Krylov subspace solver BiCGS with a Jacobi preconditioner is employed to solve the resulting system of equations. The discretization of the stress tensor can handle viscosity variations of up to 8 orders of magnitude from cell to cell and up to 45 orders of magnitude system wide. As an application to purely internally heated mantle convection in a spherical shell a parameter study of 88 cases is carried out to derive scaling laws for heat transport stagnant lid thickness and structural complexity...