This paper presents an adaptive multigrid approach, combining adaptive local grid refinement and multigrid methods, in conjunction with the Lagrangian–Eulerian finite element method to simulate contaminant transport in the 3D subsurface. Adaptive local grid refinement can improve solution accuracy without sacrificing computational efficiency because computer efforts are focused on the rough reg...

Electricity production currently generates approximately 25% of greenhouse gas emissions in the USA. Thus, increasing amount renewable energy is a key step to carbon neutrality. However, integrating large fluctuating generation significant challenge for power grid operating and planning. Grid reliability, i.e., an ability meet operational constraints under fluctuations, probably most important ...

We report on the latest additions to our open-source, block-grid adaptive framework MPI-AMRVAC , which is a general toolkit for especially hyperbolic/parabolic partial differential equations (PDEs). Applications traditionally focused shock-dominated, magnetized plasma dynamics described by either Newtonian or special relativistic (magneto)hydrodynamics, but its versatile design easily extends d...