Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time τ and the lattice spacing. The analytic solutions are the exact representation of these two flows without an...

We construct new analytical solutions of the 3 1 -dimensional modified KdV-ZakharovKuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary para...

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framewo...

The evaluation of possible leakage pathways from CO2 storage operations requires attention to the magnitude, concentration and timescales involved. Herein we discuss a problem related to CO2 storage, the migration of CO2 as it is injected. This is accomplished through the application of analytical solutions. In particular, we derive a new analytical insight into the problem of fluid injection i...

We introduce an improved second-order discretization method for the convection-reaction equation by combining analytical and numerical solutions. The method is derived from Godunov’s scheme, see [15] and [21], and uses analytical solutions to solve the one-dimensional convection-reaction equation. We can also generalize the second-order methods for discontinuous solutions, because of the analyt...

In the present study, analytical solutions for thermally developing flows in porous media under local thermal non-equilibrium (LTNE) condition are derived for different fundamental models. The analytical solutions are validated by comparison with the numerical results. Based on the analytical solutions, the local Nusselt number is obtained, and the dimensionless thermal entry length nc is predi...

The closed-form analytical solutions and semi-analytical solutions of capture times to horizontal wells are derived for di€erent recovery scenarios. The capture time is the time a ̄uid particle takes to ̄ow to the well. The ®rst scenario is recovery from a con®ned aquifer in which the in ̄uence of regional groundwater ̄ow upon the capture time is included. The second scenario is recovery from un...