Modelling of mantle flows with sharp viscosity contrasts in a viscoelastic medium is a challenging computational problem in geodynamics because of its multiple-scale nature in space and time. We have employed a recently developed adaptive multilevel wavelet collocation algorithm to study the dynamics of a small rising diapir interacting with a stiff lithosphere in a Maxwell viscoelastic mantle. In this kinematic model we have prescribed the upward velocity of the diapir and then we need to integrate in time only the momentum equation governing the temporal evolution of the pressure, stress and velocity components, which together constitute a sixth-order system in time. The total number of collocation points did not exceed 104, compared to more than 106 gridpoints using conventional evenly spaced grid methods. The viscosity of the diapir is 10-4 times lower than that of the surrounding mantle, while the viscosity of the thin lithosphere, about 5-10 per cent of the entire layer depth, is 104-108 times stiffer than the ambient mantle. Our results demonstrate the efficacy of wavelets to capture the sharp gradients of the stress and pressure fields developed in the diapiric impingement process. The interaction of the viscoelastic lithosphere with the rising viscoelastic diapir results in the localization of stress within the lithosphere. The magnitude of the stress fields can reach around 100-300 MPa. Our simple kinematic model shows clearly that viscoelasticity can potentially play an important role in the dynamics of the lithosphere, especially concerning the potential severage of the lithosphere by mantle upwellings.
- Numerical methods