0
votes
0answers
74 views

Formal Solution of Cauchy Problem: Advection Diffusion Equation

I am trying to follow a paper by Lebedev and Turitsyn http://arxiv.org/pdf/nlin/0309019v1.pdf and have become stuck very early. I am trying to see that $ ...
5
votes
2answers
265 views

Integrating pressure with respect to time

I am trying to work through the math derivation presented in a paper about gas flowing through rock due to a pressure differential across the length of rock. This is my first post so forgive me if I ...
1
vote
1answer
180 views

Velocity Verlet Integration for SPH Fluids

I am trying to implement a SPH (Smoothed Particle Hydrodynamics) based fluid solver and would like to use a second order integration method, for updating velocities and positions of the fluid ...
0
votes
1answer
212 views

How to integrate twice of this viscous term?

I am reading a paper, and I do not understand why the author said the following term when integrated twice will become, $\int\limits_\Omega {{\rm{d}}\Omega {{\bf{\psi }}^{\bf{u}}}\cdot\nabla ...