The numerical simulation of a level IV fugacity model coupled to a dispersion-advection equation to simulate the environmental concentration of a pesticide in rice fields is presented. The model simulates the dynamic distribution of the pesticide in a compartmental system constituted by air, water, rice plants and bottom sediment together with saturated soil layers. The level IV fugacity model ...

If we consider a finite difference method simply as a set of equations containing a small parameter (the grid spacing), it is evident that the tools of asymptotic analysis can give us useful information about the method. The applicability of this approach for studying consistency, long time behavior and stability is demonstrated. As example, we use a simple lattice Boltzmann scheme for the 1D a...

Abstract: Solving or approximating the advection-diffusion/dispersion equation (ADE) is a challenging and important problem and has thus motivated a great deal of intense research. A specific complication arises from the nature of the governing partial differential equation: it is characterized by a hyperbolic non-dissipative advective transport term, a parabolic dissipative diffusive (dispersi...

Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II . The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance and one elliptic equation to recover ...

An extension of the finite element method–flux corrected transport stabilization for hyperbolic problems in the context of partial differential–algebraic equations is proposed. Given a local extremum diminishing property of the spatial discretization, the positivity preservation of the one-step θ-scheme when applied to the time integration of the resulting differential–algebraic equation is sho...

This work presents a new adaptive multilevel approximation of the gradient operator on a recursively refined spherical geodesic grid. The multilevel structure provides a simple way to adapt the computation to the local structure of the gradient operator so that high resolution computations are performed only in regions where singularities or sharp transitions occur. This multilevel approximatio...

We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we...

The first part of this talk is dedicated to the introduction of the nonlinear Galerkin method applied to the Navier-Stokes equation on the rotating sphere. The Navier-Stokes equation plays a fundamental role in meteorology by modelling meso-scale (stratified) atmospherical flows. The nonlinear Galerkin method is implemented by using type three vector spherical harmonics, and convergence is sket...

Abstract. An operator-splitting algorithm is presented for the solution of a partial differential equation arising in the modeling of deposition processes in sand mechanics. Sand piles evolution is modeled by an advection-diffusion equation, with a non-smooth diffusion operator that contains a point-wise constraint on the gradient of the solution. Piecewise linear finite elements are used for t...

In previous work, a new adaptive meshfree advection scheme for numerically solving linear transport equations has been proposed. The scheme, being a combination of an adaptive semi-Lagrangian method and local radial basis function interpolation, is essentially a method of backward characteristics. The adaptivity of the meshfree advection scheme relies on customized rules for the refinement and ...