Fluid plays a pivotal role in triggering and inducing seismic events. However, the effect of fluid on the co-seismic rupture process remains largely unknown. To this end, we develop a fully dynamic spontaneous rupture model specific for fluid-related seismic events. Central to our model is the consideration of the fluid effect that accumulates over the previous quasi-static phase until the onset of rupture. This effect is resolved in two manners, including a fluid-solid decoupled approach and fluid-solid fully coupled poroelastic approach. Correspondingly, the resulting fault fluid pressure and poroelastic stress at their respective time of rupture onset is passed to the dynamic model via the fault boundary condition that follows a slip-weakening law. Under the assumption of an undrained co-seismic fluid-solid system, we then discretize the fully dynamic Cauchy equation of motion using a split-node finite element method in space and a fully implicit Newmark family finite difference method in time; a fully implicit Newton-Raphson scheme is implemented iteratively for linearizing the nonlinear equation within each time step, and a novel non-stationary preconditioner is designed to accelerate the convergence of a selected iterative linear solver. Using the above computational model, we perform several numerical experiments. Triggered and induced seismic events are simulated by designing different fault initial stress in relation to its peak and residual strength. The results suggest that, (1) both triggered and induced seismic events can undergo a supershear rupture process with a rupture velocity near the P-wave velocity, owing to a reduced seismic ratio due to the fluid effect, (2) compared to a tectonic earthquake, triggered and induced seismic events are associated with radically different wave fields, and (3) in the coupled approach, the wave field can also become asymmetric due to different poroelastic stress on the two sides of the fault at the onset of rupture.