Theory - Continuity Equation Derivation
As some of you might know, there is a lot of possibilities to discretize equations in SPH. The way I have tried to do it is by starting with the lagrangian equation for continuity:
Then I have discretized using SPH methodology as such
And to my understanding this is mathematically correct. Comparing with the formulation in DualSPHysics wiki
So this is extremely similar to what I got, but the difference is that I have "rhoi" and "Vj", so I cannot construct "mj" (mb in picture). The rest is the same though. Could anyone kindly show me how the one used in DualSPHysics was derived?