Numerical schemes for a pseudo-parabolic Burgers equation: Discontinuous data and long-time behaviour. (English) Zbl 1154.76036
Summary: We consider a simplified model for vertical non-stationary groundwater flow, which includes dynamic capillary pressure effects. Specifically, we consider a viscous Burgers-type equation that is extended with a third-order term containing mixed derivatives in space and time. We analyse the one-dimensional boundary value problem and investigate numerically its long-time behaviour. The numerical schemes discussed here take into account possible discontinuities of the solution.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76D99 | Incompressible viscous fluids |
| 35Q35 | PDEs in connection with fluid mechanics |
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