Simulating military conflict with a continuous flow model

A continuous flow model of infantry behaviour in military conflict is proposed, combining a crowd flow model based on conservation of individuals, empirical data on walking speed under varying crowd density and surface inclination, and a variation of the Lanchester attrition model to account for casualties. Both close-in combat and ranged fire are incorporated in the model. In order to implement relative movement and orientation of a unit, an additional variable is introduced that tracks the identity of a subunit within an overall unit. This approach to subunit modelling represents a new contribution to the literature. Further, we offer two new models of how ground troops adjust their walking behaviour to the terrain. Example numerical solutions of the multi-group crowd flow equation with an attrition source term are presented. Conventional implicit, second-order, upwind methods for convection-diffusion equations are employed in the calculations. The model is seen to produce behaviour that could plausibly depict infantry combat. An advancing force tends to pile up in the rear and stretch out in the front, and interacting armies tend to form a linear front. Unit reorientation and a breakpoint are illustrated in an example scenario. We propose that modelling battlefield dynamics as a continuous flow may provide strategic decision makers with a more intuitive understanding of the momentum of a conflict, and reduce the quantity of information that a human observer needs to assess the flow of battle.