The method development process in liquid chromatography (LC) involves optimization of a variety of method parameters including stationary phase chemistry, column temperature, initial and final mobile phase compositions, and gradient time when gradient mobile phases are used. Here, a general simulation program to predict the results (i.e., retention time, peak width and peak shape) of LC separations, with the ability to study various complex chromatographic conditions is described. The simulation program is based on the Craig distribution model where the column is divided into discrete distance (Δz) and time (Δt) segments in a grid and is based on parameterization with either the linear solvent strength or Neue-Kuss models for chromatographic retention. This algorithm is relatively simple to understand and produces results that agree well with closed form theory when available. The set of simulation programs allows for the use of any eluent composition profile (linear and nonlinear), any column temperature, any stationary phase composition (constant or non-constant), and any composition and shape of the injected sample profile. The latter addition to our program is particularly useful in characterizing the solvent mismatch effect in comprehensive two-dimensional liquid chromatography (2D-LC), in which there is a mismatch between the first dimension (1D) effluent and second dimension (2D) initial mobile phase composition. This solvent mismatch causes peak distortion and broadening. The use of simulations can provide a better understanding of this phenomenon and a guide for the method development for 2D-LC. Another development that is proposed to have a great impact on the enhancement of 2D-LC methods is the use of continuous stationary phase gradients. When using rapid mobile phase gradients in the second dimension separation with diode array detection (DAD), refractive index changes cause large backgrounds such as an injection ridge (from solvent mismatch) and sloping baselines which can be problematic for achieving accurate quantitation. Use of a stationary phase gradient may enable the use of an isocratic mobile phase in the 2D, thus minimizing these background signals. Finally, our simulator can be used as an educational tool. Unlike commercially available simulators, our program can capture the evolution of the chromatogram in the form of movies and/or snapshots of the analyte distribution over time and/or distance to facilitate a better understanding of the separation process under complicated circumstances. We plan to make this simulation program publically available to all chromatographers and educators to aid in more efficient method development and chromatographic training.