Actin and microtubules are components of the cytoskeleton, and are key mediators of neuron growth and maintenance. Knowing how they are regulated enhances our understanding of neural development, ageing, degeneration and regeneration. However, biological investigation alone will not unravel the complex cytoskeletal machinery. We expect that inquiries about the cytoskeleton can be significantly enhanced if their physicochemical behavior is concealed and summarized in mathematical and computational models that can be coupled to concepts of biological regulation. Our computational modeling concerns the mechanical aspects associated with the dynamics of relatively simple, finger-like membrane protrusions called filopodia. Here we propose an alternative approach for representing the displacement of molecules and cytoplasmic fluid in the extremely narrow and long filopodia and discuss strategies to couple the particle-in-cell method with algorithms for laminar flow to model the two phases of actin dynamics: polymerization into filaments which are pulled back into the cell and compensatory G-actin drift towards its tip to supply polymerization. We use nerve cells of the fruit fly Drosophila as an effective, genetically amenable biological system to generate experimental data as the basis for the abstract models and their validation.