A Progressive Asymptotic Approach Procedure for Simulating Steady-State Natural Convective Problems in Fluid-Saturated Porous Media -- A Consistent Point-Searching Interpolation Algorithm for Simulating Coupled Problems between Deformation, Pore-Fluid Flow, Heat Transfer and Mass Transport Processes in Hydrothemal Systems -- A Term Splitting Algorithm for Simulating Fluid-Rock Interaction Problems in Fluid-Saturated Hydrothermal Systems of Subcritical Zhao Numbers -- A Segregated Algorithm for Simulating Chemical Dissolution Front Instabilities in Fluid-Saturated Porous Rocks -- A Decoupling Procedure for Simulating Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions in Fluid-Saturated Porous Rocks -- An Equivalent Source Algorithm for Simulating Thermal and Chemical Effects of Intruded Magma Solidification Problems -- The Particle Simulation Method for Dealing with Spontaneous Crack Generation Problems in Large-Scale Geological Systems. This monograph aims to provide state-of-the-art numerical methods, procedures and algorithms in the field of computational geoscience, based on the authors' own work during the last decade. Although some theoretical results are provided to verify numerical ones, the main focus of this monograph is on computational simulation aspects of the newly-developed computational geoscience discipline. The advanced numerical methods, procedures and algorithms presented are also applicable to a wide range of problems in both geological length-scales and engineering length-scales. In order to broaden the readership, common mathematical notations are used to describe the theoretical aspects of geoscience problems, making it either an invaluable textbook for postgraduate students or an indispensable reference book for computational geoscientists, mathematicians, engineers and geoscientists.