The transport and continuum equations exhibit a number of conservation laws. For example, scalar multiplication is conserved by the transport equation, while positivity of probabilities is conserved by the continuum equation. Certain discretization techniques, such as particle based methods, conserve these properties, but converge slower than spectral discretization methods on smooth data. Stan...

In this paper we present a new one-particle Monte Carlo iteration scheme to self-consistently take into account generation-recombination processes as well as quantum corrections. The basic idea is to couple the Boltzmann transport equation (or the Boltzmann-Wigner equation) not only with the Poisson equation, but also with the continuity equation by using exact transport coefficients from the M...

In nuclear reactor design, the most fundamental task is to follow the neutron distribution as a function of space, direction, energy and time, in order to maintain and control the nuclear fission chain reaction. The fundamental equation governing the average behaviour of neutrons is given by the linear form of Boltzmann transport equation, which is an integro-differential equation. The core sim...

Aiming at a description of transport processes where the dynamically generated width of the states is potentially large a transport equation beyond the quasiparticle approximation is derived in first order gradient expansion. An effective particle number is identified which is exactly conserved by the coarse grained transport equation. Using a test particle ansatz for this conserved quantity al...

Reactive transport describes the coupling among flow, transport and chemical reactions occurring in porous media; and therefore it is important in areas such as aquifer remediation, groundwater contamination, geochemical reaction modeling and CO2 sequestration. Due to the large time scales involved and/or the lack of accessibility to the subsurface, in most of these studies an adequate represen...

Abstract We present a new connection between the classical theory of full and truncated moment problems partial differential equations, as follows. For heat equation $\partial _t u = {\nu } \Delta u$, with initial data $u_0 \in {\mathcal {S}}(\mathds {R}^n)$, we first compute moments $s_{\alpha }(t)$ unique solution $u {R}^n)$. These are polynomials in time variable, degree comparable to $\alph...

In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...

In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...

One of the principal barriers in developing accurate and tractable predictive models turbulent flows with a large number species is to track every by solving separate transport equation, which can be computationally impracticable. In this paper, we present an on-the-fly reduced order modeling reactive as well passive equations reduce computational cost. The presented approach seeks low-rank dec...