<p>We present a high-performance numerical algorithm for simulating the dissolution of porous media based on the Darcy-Brinkman model. The code utilizes recent developments in the lattice Boltzmann method to achieve high stability and performance gains. To the best of our knowledge, this is the first use of the lattice Boltzmann method as a fixed-point solver for problems with significant time-scale separation. The simulations enable the study of the development of reactive-infiltration instabilities in heterogeneous media, particularly in natural rocks, at high spatial resolutions. They reveal the formation and growth of highly conductive dissolution channels (wormholes), as well as the competition between them for flow and reactant flux. The transition from Darcy to Stokes flow is observed within the dissolution channels. We argue that there exists a minimum resolution at which the simulations need to be run in order to obtain a faithful representation of the geometry of the dissolution channels. At lower resolutions, the channels become straight, bulkier, and less ramified. We show that this minimum resolution is associated with the correlation length of the porosity field, establishing a critical link for accurate simulation fidelity. The results demonstrate the potential of next-generation supercomputers, based on GPGPU-based parallel computation, for predictive simulation of dissolution processes in porous media at experimentally relevant length scales and high resolutions.</p>