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...

We show that the solution of the Burgers equation can be approximated in LX(R), to within 0(m~1/*(lnm)2), by a random walk method generated by 0(m) particles. The nonlinear advection term of the equation is approximated by advecting the particles in a velocity field induced by the particles. The diffusive term is approximated by adding an appropriate random perturbation to the particle position...

In this work we propose a new Eulerian method for handling the dynamics of a liquid and its surface attributes (for example its color). Our approach is based on a new method for interface advection that we term the Marker Level Set (MLS). The MLS method uses surface markers and a level set for tracking the surface of the liquid, yielding more efficient and accurate results than popular methods ...

The numerical investigation of large bubbles rising under an inclined plane is presented. A numerical method for the simulation of fluid flows with complex free surfaces is presented, in which the liquid is assumed to be Newtonian, while gas bubbles are assumed to be compressible. A volume-of-fluid method is used to track the liquid domain. A time splitting algorithm allows to decouple the adve...

The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation ordering in a multigrid cycle with appropriate residual weighting leads to an effic...

Time integration of advection dominated advection–diffusion problems on refined meshes can be a challenging task, since local refinement lead to severe time step restriction, whereas standard implicit stepping is usually hardly suitable for treating terms. We show that exponential integrators an efficient, yet conceptually simple, option in this case. Our comparison includes three and one conve...

Saul’yev-type asymmetric schemes have been widely used in solving diffusion and advection equations. In this work, we show that Saul’yev-type schemes can be derived from the exponential splitting of the semidiscretized equation which fundamentally explains their unconditional stability. Furthermore, we show that optimal schemes are obtained by forcing each scheme’s amplification factor to match...

In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The method solves stationary advection-dominated diffusion problems. We stabilize via residual minimization. discretize problem using B-spline basis functions. then seek to minimize isogeometric over a spline space built on tensor product mesh. construct solution smooth subspace of residual. can specify by reducin...