Systems and methods to simulate joining operations are disclosed. An example computer-implemented system for simulation of joining materials with or without filler material, includes: processing circuitry; and a machine readable storage device storing machine readable instructions which, when executed by the processing circuitry, cause the processing circuitry to display a visual simulation of a three-dimensional joining operation within a simulation domain by simulating the simulation domain as a set of interconnected cross-sectional two dimensional slices.