Models for reacting flow are typically based on advection-diffusion-reaction (A-D-R) partial differential equations. Many practical cases correspond to situations where the relevant time-scales associated with each of the three sub-processes can be widely different, leading to disparate time-step requirements for robust and accurate timeintegration. In particular, interesting regimes in combust...

In this paper, we study the propagation speeds of reaction-diffusion-advection (RDA) fronts in time-periodic cellular and chaotic flows with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We first apply variational principle to reduce computation KPP front a principal eigenvalue problem linear advection-diffusion operator space-time periodic coefficients on domain. To end, develop efficient ...

In this article we describe two areas of recent progress in the construction of accurate and robust ®nite di€erence algorithms for continuum dynamics. The support operators method (SOM) provides a conceptual framework for deriving a discrete operator calculus, based on mimicking selected properties of the di€erential operators. In this paper, we choose to preserve the fundamental conservation l...

River ecosystems are the prime example of environments where unidirectional flow influences the dispersal of individuals. Spatial patterns of community composition and species replacement emerge from complex interplays of hydrological, geochemical, biological, and ecological factors. Local processes affecting algal dynamics are well understood, but a mechanistic basis for large scale emerging p...

A time-splitting approach for advection–dispersion equations is considered. The dispersive and advective fluxes are split into two separate partial differential equations (PDEs), one containing the dispersive term and the other one the advective term. On triangular elements a triangle-based high resolution Finite Volume (FV) scheme for advection is combined with a Mixed Hybrid Finite Element (M...

In this note we consider proper ways to combine numerical schemes for advective transport and nonlinear chemistry. Obvious combinations are obtained with splitting in a so-called fractional step approach. We shall discuss for this approach correct implementations of source terms and innow boundary conditions. Further we consider the use of multistep methods with explicit treatment of the advect...

In population balance equations, the distribution of the entities depends not only on space and time but also on their own properties referred to as internal coordinates. The operator splitting method is used to transform the whole time-dependent problem into two unsteady subproblems of a smaller complexity. The first subproblem is a timedependent convection-diffusion problem while the second o...

In this paper, we study the asymptotic profile of the steady state of a reactiondiffusion-advection model in ecology proposed in [13, 17]. The model describes the population dynamics of a single species experiencing a uni-directional flow. We show the existence of one or more internal transition layers and determine their locations. Such locations can be understood as the upstream invasion limi...

A spectral-Lagrangian deterministic solver for the Boltzmann equation for rarefied gas flows is proposed. Numerical solutions are obtained for the flow across normal shock waves of pure gases and mixtures by means of a time-marching method. Operator splitting is used. The solution update is obtained as a combination of the operators for the advection (or transport) and homogeneous (or collision...

In this article, we investigate the application of an operatorsplitting/finite element method to the numerical simulation of a liquid crystal flow. The operator-splitting is achieved through three stages, so that each stage is simpler and easier to deal with than the step of any un-split implicit scheme. The first stage deals with the system coupling a Stokes equation for velocity with an equat...