A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations

summary:A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations is presented. Applying the orthogonal projection technique, we introduce two local Gauss integrations as a stabilizing term in the error correction method, and derive a new error correction method. In both the coarse solution computation step and the error computation step, a locally stabilizing term based on two local Gauss integrations is introduced. The stability and convergence of the new error correction algorithm are established. Numerical examples are also presented to verify the theoretical analysis and demonstrate the efficiency of the proposed method

Mathematical Aspects of Computational Fluid Dynamics

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Advanced flamelet modelling of turbulent non-premixed and partially premixed combustion

Current work focuses on the development and performance evaluation of advanced flamelet models for turbulent non-premixed and partially premixed combustion in RANS and large eddy simulation (LES) based modelling. A RANS-based combustion modelling strategy which has the ability to capture the detailed structure of turbulent non-premixed flames, including the pollutant NO, and account for the effects of radiation heat loss and transient evolution of NO, has been developed and incorporated into the in-house RANS code. The strategy employs an 'enthalpy defect'-based non-adiabatic flamelet model in conjunction with steady or unsteady nonadiabatic flamelets based NO submodels. [Continues.

Advanced flamelet modelling of turbulent nonpremixed and partialy premixed combustion

Current work focuses on the development and performance evaluation of advanced flamelet models for turbulent non-premixed and partially premixed combustion in RANS and large eddy simulation (LES) based modelling. A RANS based combustion modelling strategy which has the ability to capture the detailed structure of turbulent non-premixed flames, including the pollutant NO, and account for the effects of radiation heat loss and transient evolution of NO, has been developed and incorporated into the in-house RANS code. The strategy employs an 'enthalpy-defect' based non-adiabatic flamelet model in conjunction with steady or unsteady nonadiabatic flamelets based NO submodels. The performanceo f the non-adiabaticm odel and its NO submodelsh asb eena ssessed against experimental measurements and steady flamelet model predictions for turbulent CH4/H2 bluff-body stabilized and CH4-air piloted jet flames. Appreciable improvements in the mean thermal structure predictions have been observed in the piloted jet flames by consideration of radiation heat loss through the non-adiabatic flamelet model. Since transient effects were weaker in the piloted jet flame, both unsteady and steady non-adiabatic NO submodels provided similar level of improvement in the pollutant NO predictions in comparison to their adiabatic counterpartsT. ransiente ffectsw ere, however,d ominanti n the bluff-body flame. The unsteady non-adiabatic NO submodel provided excellent agreement with measured NO distribution in comparison to the appreciably overpredicted distribution by its steadyc ounterpart.T he strategyo f non-adiabaticf lamelet model in conjunctionw ith unsteady non-adiabatic NO submodel seems to provide an accurate and robust alternative to the conventional strategy of steady flamelet model with steady NO submodel. While addressing the limitations of steady flamelet model in regard to radiation and slow chemistry of NO is one objective of this research, extending the applicability of the model to partially premixed combustion has been pursued as the second objective. Flamelet/progress variable (FPV) approach based combustion models, which have the potential to describe both non-premixed and partially premixed combustion, have been incorporated in the in-house RANS and LES codes. Based on the form of the PDF for reaction progress variable, two different formulations, FPV-8 function model and FPV-P function model, have been derived. (Continues...)

Mathematical Architecture for Models of Fluid Flow Phenomena

This thesis is a study of several high accuracy numerical methods for fluid flow problems and turbulence modeling.First we consider a stabilized finite element method for the Navier-Stokes equations which has second order temporal accuracy. The method requires only the solution of one linear system (arising from an Oseen problem) per time step. We proceed by introducing a family of defect correction methods for the time dependent Navier-Stokes equations, aiming at higher Reynolds' number. The method presented is unconditionally stable, computationally cheap and gives an accurate approximation to the quantities sought. Next, we present a defect correction method with increased time accuracy. The method is applied to the evolutionary transport problem, it is proven to be unconditionally stable, and the desired time accuracy is attained with no extra computational cost. We then turn to the turbulence modeling in coupled Navier-Stokes systems - namely, MagnetoHydroDynamics. Magnetically conducting fluids arise in important applications including plasma physics, geophysics and astronomy. In many of these, turbulent MHD (magnetohydrodynamic) flows are typical. The difficulties of accurately modeling and simulating turbulent flows are magnified many times over in the MHD case. We consider the mathematical properties of a model for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows. We prove existence, uniqueness and convergence of solutions for the simplest closed MHD model. Furthermore, we show that the model preserves the properties of the 3D MHD equations. Lastly, we consider the family of approximate deconvolution models (ADM) for turbulent MHD flows. We prove existence, uniqueness and convergence of solutions, and derive a bound on the modeling error. We verify the physical properties of the models and provide the results of the computational tests

Uzawa smoother in multigrid for the coupleD porous medium and stokes flow system

The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss–Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, local Fourier analysis is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs very well for small values of the hydraulic conductivity and fluid viscosity, which are relevant for applications