Digital microfluidic biochips provide a controlled and miniaturized environment to carry out biochemical protocols in an automated fashion. Software-based simulators are essential tools that aid the design of such protocols by enabling users to verify correct execution before targeting the physical biochip. To produce a simulation that is faithful to reality, the fluidic behavior of the droplets and their interaction with the driving electrodes must be taken into account. This paper presents a framework for simulating DMF biochips in a resource-constrained web-based environment. The framework is based on a novel droplet model that uses logic-based calculations to capture fluidic behavior. Thus, enabling to faithfully simulate the movement, merging, and splitting of arbitrary-shaped droplets with a low-computational footprint. The simulation framework also includes modular component models to capture the behavior of sensors and actuators, an event-driven simulation engine, and a graphical user interface. The framework is implemented as a client-side web application and runs in a browser. The evaluation carried out using artificial and real-life test cases shows that the framework can deliver real-time simulations with a high level of fidelity.