where: x is position in one or more spatial dimensions; u(x, t) is some scalar or vector field, such as fluid velocity and pressure; L is a dissipative linear operator, such as ∇; f(u) includes other autonomous terms representing nonlinear advection, reaction, etc.; and q(u, t) is some time dependent control or possibly stochastic forcing [22]. Among many physically relevant examples are Burger...

Torque fluctuations due to magnetorotational turbulence in proto-planetary disks may greatly influence the migration patterns and survival probabilities of nascent planets. Provided that the turbulence is a stationary stochastic process with finite amplitude and correlation time, the resulting diffusive migration can be described with a FokkerPlanck equation, which we reduce to an advection-dif...

In this paper, the piecewise parabolic method is presented for solving one-dimensional advection-diffusion type equation and its application to burger equation. First, given solution domain discretized by using a uniform Discretization grid point. Next applying integration in terms of spatial variable, we converting it into system first-order ordinary differential temporarily variable. Next, Ta...

A method for solving the saturation equation for two-phase ow is presented. The method may be viewed as an operator splitting method or as an Eulerian-Lagrangian backtracking procedure or as a modiied method of characteristics. For each time step, the method consists of an advection step and a diiusion step. The advection step requires the tracking of streamlines locally around certain integrat...

The advection equation is used to model the transport of material whose mass is conserved. If the vector field governing the advection is divergence-free, then the advection equation reduces to the usual transport equation which is used to model linear diffusion processes such as transport of neutrons, scattering of light and propagation of -rays in a scattering medium [1]. The uncontrolled adv...

A two-step interface capturing scheme, implemented within the framework of conservative level set method, is developed in this study to simulate the gas/water two-phase fluid flow. In addition to solving the pure advection equation, which is used to advect the level set function for tracking interface, both nonlinear and stabilized features are taken into account for the level set function so t...

The governing equation of longitudinal dispersion phenomenon of one-dimensional concentration distribution in fluid flow through porous media has been obtained in term of one-dimensional non-linear advection-diffusion equation. This equation has been converted in term of dimensionless non-linear Burger's equation with its derivative, and it is multiplied by small parameter   0,1   . This eq...