EFFICIENT COMPUTATION OF COORDINATE-FREE MODELS OF FLAME FRONTS

2021 ◽  
pp. 1-12 ◽  
Author(s):  
B. F. AKERS ◽  
D. M. AMBROSE
Keyword(s):  
Flame Front ◽  
Nonlinear Models ◽  
Numerical Procedure ◽  
Front Propagation ◽  
Computational Method ◽  
Efficient Computation ◽  
Vortex Sheets ◽  
Weakly Nonlinear ◽  
Free Model ◽  
Sivashinsky Equation

AbstractWe present an efficient, accurate computational method for a coordinate-free model of flame front propagation of Frankel and Sivashinsky. This model allows for overturned flames fronts, in contrast to weakly nonlinear models such as the Kuramoto–Sivashinsky equation. The numerical procedure adapts the method of Hou, Lowengrub and Shelley, derived for vortex sheets, to this model. The result is a nonstiff, highly accurate solver which can handle fully nonlinear, overturned interfaces, with similar computational expense to methods for weakly nonlinear models. We apply this solver both to simulate overturned flame fronts and to compare the accuracy of Kuramoto–Sivashinsky and coordinate-free models in the appropriate limit.

Efficient computation of coordinate-free models of flame fronts

2021 ◽  
Vol 63 ◽  
pp. 58-69
Author(s):  
Benjamin Akers ◽  
D. M. Ambrose
Keyword(s):  
Flame Front ◽  
Nonlinear Models ◽  
Numerical Procedure ◽  
Front Propagation ◽  
Computational Method ◽  
Efficient Computation ◽  
Vortex Sheets ◽  
Weakly Nonlinear ◽  
Free Model ◽  
Sivashinsky Equation

We present an efficient, accurate computational method for a coordinate-free model of flame front propagation of Frankel and Sivashinsky. This model allows for overturned flames fronts, in contrast to weakly nonlinear models such as the Kuramoto–Sivashinsky equation. The numerical procedure adapts the method of Hou, Lowengrub and Shelley, derived for vortex sheets, to this model. The result is a nonstiff, highly accurate solver which can handle fully nonlinear, overturned interfaces, with similar computational expense to methods for weakly nonlinear models. We apply this solver both to simulate overturned flame fronts and to compare the accuracy of Kuramoto–Sivashinsky and coordinate-free models in the appropriate limit.   doi:10.1017/S1446181121000079

Metastability for a generalized Burgers equation with applications to propagating flame fronts

1999 ◽  
Vol 10 (1) ◽  
pp. 27-53 ◽  
Author(s):  
X. SUN ◽  
M. J. WARD
Keyword(s):  
Flame Front ◽  
Principal Eigenvalue ◽  
Vertical Channel ◽  
Front Propagation ◽  
Slow Motion ◽  
Diffusion Limit ◽  
Asymptotic Results ◽  
Small Diffusion ◽  
Generalized Burgers Equation ◽  
Exponentially Small

In the small diffusion limit ε→0, metastable dynamics is studied for the generalized Burgers problemformula hereHere u=u(x, t) and f(u) is smooth, convex, and satisfies f(0)=f′(0)=0. The choice f(u)=u2/2 has been shown previously to arise in connection with the physical problem of upward flame-front propagation in a vertical channel in a particular parameter regime. In this context, the shape y=y(x, t) of the flame-front interface satisfies u=−yx. For this problem, it is shown that the principal eigenvalue associated with the linearization around an equilibrium solution corresponding to a parabolic-shaped flame-front interface is exponentially small. This exponentially small eigenvalue then leads to a metastable behaviour for the time- dependent problem. This behaviour is studied quantitatively by deriving an asymptotic ordinary differential equation characterizing the slow motion of the tip location of a parabolic-shaped interface. Similar metastability results are obtained for more general f(u). These asymptotic results are shown to compare very favourably with full numerical computations.

scholarly journals Flame Front Propagation in an Optical GDI Engine under Stoichiometric and Lean Burn Conditions

Energies ◽  
2017 ◽  
Vol 10 (9) ◽  
pp. 1337 ◽  
Author(s):  
Santiago Martinez ◽  
Adrian Irimescu ◽  
Simona Merola ◽  
Pedro Lacava ◽  
Pedro Curto-Riso
Keyword(s):  
Flame Front ◽  
Front Propagation ◽  
Lean Burn ◽  
Gdi Engine

Random Collocation Method (RCM)

2010 ◽  
Author(s):  
Hiroshi Isshiki
Keyword(s):  
Numerical Method ◽  
Collocation Method ◽  
Analytical Method ◽  
Traditional Method ◽  
Analytical Approach ◽  
Numerical Procedure ◽  
Computational Method ◽  
Weak Point ◽  
The Past ◽  
Innovative Idea

Recently, young people’s concern on theory is becoming very poor. If there is a numerical procedure that is friendlier with theory, the distance between theory and calculation would be decreased much, and the interaction between them would become more active. When the geometry of the domain is simple, the traditional analytical method using function expansion is very convenient in many numerical problems. In many problems, it has given very useful solutions for various problems. However, its effectiveness is usually limited to simple geometries of the domain. In the past, a fusion of the analytical approach and computational one has not been pursued sufficiently. If it becomes possible, it may give a different paradigm for obtaining the numerical solution. In the present paper, an innovative idea named Random Collocation Method (RCM) is discussed on how to overcome the weak point of the traditional method by combining it with computational method. It is the purpose of the present paper to develop the simplest numerical method and to make the distance between the theory and numerical method as small as possible.

Fully nonlinear internal waves in a two-fluid system

1999 ◽  
Vol 396 ◽  
pp. 1-36 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
ROBERTO CAMASSA
Keyword(s):  
Solitary Wave ◽  
Euler Equations ◽  
Deep Water ◽  
Large Amplitude ◽  
Nonlinear Models ◽  
Weak Nonlinearity ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
The Waves ◽  
Two Fluid

Model equations that govern the evolution of internal gravity waves at the interface of two immiscible inviscid fluids are derived. These models follow from the original Euler equations under the sole assumption that the waves are long compared to the undisturbed thickness of one of the fluid layers. No smallness assumption on the wave amplitude is made. Both shallow and deep water configurations are considered, depending on whether the waves are assumed to be long with respect to the total undisturbed thickness of the fluids or long with respect to just one of the two layers, respectively. The removal of the traditional weak nonlinearity assumption is aimed at improving the agreement with the dynamics of Euler equations for large-amplitude waves. This is obtained without compromising much of the simplicity of the previously known weakly nonlinear models. Compared to these, the fully nonlinear models' most prominent feature is the presence of additional nonlinear dispersive terms, which coexist with the typical linear dispersive terms of the weakly nonlinear models. The fully nonlinear models contain the Korteweg–de Vries (KdV) equation and the Intermediate Long Wave (ILW) equation, for shallow and deep water configurations respectively, as special cases in the limit of weak nonlinearity and unidirectional wave propagation. In particular, for a solitary wave of given amplitude, the new models show that the characteristic wavelength is larger and the wave speed is smaller than their counterparts for solitary wave solutions of the weakly nonlinear equations. These features are compared and found in overall good agreement with available experimental data for solitary waves of large amplitude in two-fluid systems.

Thermohydrodynamic Analysis of Compliant Flexure Pivot Tilting Pad Gas Bearings

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Kyuho Sim ◽  
Daejong Kim
Keyword(s):  
Boundary Conditions ◽  
Energy Equation ◽  
Numerical Procedure ◽  
Computational Method ◽  
Temperature Fields ◽  
Linear Perturbation ◽  
Gas Bearings ◽  
Thermal Boundary Conditions ◽  
Thermal Growth ◽  
Tilting Pad

A new thermohydrodynamic (THD) analysis for compliant flexure pivot tilting pad gas bearings is presented. Unlike many previous THD analyses on oil-lubricated bearings and gas bearings, the new THD analysis solves the rotor and bearing pad temperatures as well as the gas film temperature simultaneously upon adequate thermal boundary conditions on the bearing shell and rotor ends are given. All the previous studies assume that the rotor and bearing temperatures are given as thermal boundary conditions to solve 2D or 3D energy equation in the bearing film. The developed computational method is unique because these boundary conditions are found internally through global energy balance around the bearing. A numerical procedure involves solving the generalized Reynolds equation, 3D energy equation, and heat flux equations around the bearings simultaneously through iterative process. Furthermore, rotor thermal and centrifugal expansions are also considered during the iteration. Parametric studies were performed for the various temperature fields, i.e., rotor temperature, gas film temperature, and pad temperature as a function of nominal clearance, external load, and various thermal boundary conditions. Nominal clearance showed the most significant influence on overall THD behavior. The analyses also show that the rotor-bearing system can go to thermal runaway if adequate cooling mechanism does not exist. Linear perturbation analysis was also performed to investigate the thermal effects on the rotordynamic performance. Rotor thermal growth and increased viscosity increased direct stiffness and damping coefficients compared to the isothermal case.

Nonlinear effects of stretch on the flame front propagation

2010 ◽  
Vol 157 (10) ◽  
pp. 1825-1832 ◽  
Author(s):  
F. Halter ◽  
T. Tahtouh ◽  
C. Mounaïm-Rousselle
Keyword(s):  
Flame Front ◽  
Front Propagation ◽  
Nonlinear Effects
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