Laser speckle imaging (LSI) can be used to study dynamic processes in turbid media, such as blood flow. However, it is presently still challenging to obtain meaningful quantitative information from speckle, mainly because speckle is the interferometric summation of multiply scattered light. Consequently, speckle represents a convolution of the local dynamics of the medium. In this paper, we present a computational model for simulating the LSI process, which we aim to use for improving our understanding of the underlying physics. Thereby reliable methods for extracting meaningful information from speckle can be developed. To validate our code, we apply it to a case study resembling blood flow: a cylindrical fluid flow geometry seeded with small spherical particles and modulated with a heartbeat signal. From the simulated speckle pattern, we successfully retrieve the main frequency modes of the original heartbeat signal. By comparing Poiseuille flow to plug flow, we show that speckle boiling causes a small amount of uniform spectral noise. Our results indicate that our computational model is capable of simulating LSI and will therefore be useful in future studies for further developing LSI as a quantitative imaging tool.