SPH could work for this as JoeJ said. 

Material point method (MPM) may also be a good fit. Here is a recent variant of it that does really well with sand type simulations:

https://github.com/yuanming-hu/taichi_mpm

@jak6jak Sorry, my net was down - and I was too busy to fix it, both at work and here fixing bugs. Anyway. Almost like you said, but better written in dv/dt form, like dv/dt=a, where 'a' is the acceleration (F/m). Solving this finding v(t), and next integrating to get the position deltas is the key…