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SUMMARYWe construct finite volume schemes of very high order of accuracy in space and time for solving the nonlinear Richards equation (RE). The general scheme is based on a three-stage predictor-corrector procedure. First, a high-order weighted essentially non-oscillatory (WENO) reconstruction procedure is applied to the cell averages at the current time level to guarantee monotonicity in the presence of steep gradients. Second, the temporal evolution of the WENO reconstruction polynomials is computed in a predictor stage by using a global weak form of the governing equations. A global space-time DG FEM is used to obtain a scheme without the parabolic time-step restriction caused by the presence of the diffusion term in the RE. The resulting nonlinear algebraic system is solved by a Newton-Krylov method, where the generalized minimal residual method algorithm of Saad and Schulz is used to solve the linear subsystems. Finally, as a third step, the cell averages of the finite volume method are updated using a one-step scheme, on the basis of the solution calculated previously in the space-time predictor stage. Our scheme is validated against analytical, experimental, and other numerical reference solutions in four test cases. A numerical convergence study performed allows us to show that the proposed novel scheme is high order accurate in space and time.

Self-heating in compost piles results in unsuitable doors, smoke production and fires, having strong negative environmental impacts. Field, laboratory and numerical studies were accomplished trying to reproduce and understand the conditions where selfheating and combustion may take place. Inside a compost pile, built from solid obtained after municipal waste water treatment, oxygen, methane, carbon monoxide and carbon dioxide concentrations and temperature change with time and in depth. Electrical conductivity and pH showed only sligth changes. In field piles temperature increased with time until get a maximum about 90°C. While no spontaneous combustion was observed after 6 months in field experiments, in laboratory studies carried out in a closed bottom cylinder, self-ignition was observed and a maximun temperature of about 400 °C was reached.Numerical simulations describe the field piles internal heat generation, concluding that a minimum of 1.8 m height is required to reach a self-ignition condition.

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