General-purpose motion planners for automated/autonomous vehicles promise to handle the task of motion planning (including tactical decision-making and trajectory generation) for various automated driving functions (ADF) in a diverse range of operational design domains (ODDs). The challenges of designing a general-purpose motion planner arise from several factors: a) A plethora of scenarios with different semantic information in each driving scene should be addressed, b) a strong coupling between long-term decision-making and short-term trajectory generation shall be taken into account, c) the nonholonomic constraints of the vehicle dynamics must be considered, and d) the motion planner must be computationally efficient to run in real-time. The existing methods in the literature are either limited to specific scenarios (logic-based) or are data-driven (learning-based) and therefore lack explainability, which is important for safety-critical automated driving systems (ADS). This paper proposes a novel general-purpose motion planning solution for ADS inspired by the theory of fluid mechanics. A computationally efficient technique, i.e., the lattice Boltzmann method, is then adopted to generate a spatiotemporal vector field, which in accordance with the nonholonomic dynamic model of the Ego vehicle is employed to generate feasible candidate trajectories. The trajectory optimising ride quality, efficiency and safety is finally selected to calculate the imminent control signals, i.e., throttle/brake and steering angle. The performance of the proposed approach is evaluated by simulations in highway driving, on-ramp merging, and intersection crossing scenarios, and it is found to outperform traditional motion planning solutions based on model predictive control (MPC).