Reactive mass transport, in which chemical dissolution front may become unstable, is a common phenomenon in the field of groundwater hydrology. The use of mathematical transforms can convert many scientific and engineering problems from the conventional time–space domain into a generalized time–space domain, so that analytical solutions, which are impossible to be directly obtained in the conventional time–space domain, can be derived in the generalized time–space domain. The theoretical analysis and computational simulation of dissolution-timescale chemical dissolution-front instability within fluid-saturated porous media is no exception. To investigate how different mathematical transforms can affect the theoretical analyses and computational simulation of chemical dissolution-front instability within fluid-saturated porous media, two different approaches are considered to select mathematical transforms in this study. In the first approach, the mathematical transform mainly consists of a much larger timescale than the dissolution timescale and a length-scale that is independent of the mineral dissolution ratio (MDR), while in the second approach, the mathematical transform mainly consists of the dissolution timescale and the MDR-dependent length-scale. The related theoretical and computational results have demonstrated that: (1) the use of two different mathematical transforms has no effect on the analytical solution to the dispersion equation of a chemical dissolution-front instability problem in the original physical time–space domain. (2) The use of different mathematical transforms may have significant effects on computationally simulating the evolution patterns of unstable chemical dissolution-front in finite space domains, which are filled with fluid-saturated porous media. (3) If the mathematical transform is appropriately selected, then the dissolution-timescale chemical dissolution-front instability problem in fluid-saturated porous media is mathematically solvable.