0000000000020202
AUTHOR
B. Wiebe
Stochastic Galerkin method for cloud simulation
AbstractWe develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results…
IMEX Finite Volume Methods for Cloud Simulation
We present new implicit-explicit (IMEX) finite volume schemes for numerical simulation of cloud dynamics. We use weakly compressible equations to describe fluid dynamics and a system of advection-diffusion-reaction equations to model cloud dynamics. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravitational waves as well as diffusive effects and a non-stiff nonlinear part that models nonlinear advection effects. We use a stiffly accurate second order IMEX scheme for time discretization to approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. Fast microscale clou…
Numerical Simulation of a Contractivity Based Multiscale Cancer Invasion Model
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer cells coupled with microscopic dynamics of the cells adhesion on the extracellular matrix. The difficulties to overcome arise from the non-constant advection and diffusion coefficients, a time delay term, as well as stiff reaction terms.
Visualization of Parameter Sensitivity of 2D Time-Dependent Flow
In this paper, we present an approach to analyze 1D parameter spaces of time-dependent flow simulation ensembles. By extending the concept of the finite-time Lyapunov exponent to the ensemble domain, i.e., to the parameter that gives rise to the ensemble, we obtain a tool for quantitative analysis of parameter sensitivity both in space and time. We exemplify our approach using 2D synthetic examples and computational fluid dynamics ensembles.