High-order method

There are, however, additional issues when one wants to perform the LES of an industrial device, and these are to be solved if the LES methodology is ever to be a useful tool. First, the geometric intricacy of most industrial combustion chambers cannot be represented with a Cartesian mesh high-order methods on unstructured grids must be developed. Moreover, many issues about the boundary conditions are raised, such as boundary movement for blades or pistons, turbulence injection, and acoustic properties. Such challenges are not to be underestimated, as their impact on the structure of the flow might sometimes be greater than that of the turbulence model. 

This method seems at first sight unpromising, because of its low error order, the same as that for Euler. However, it has some very useful stability properties (see later) and forms the basis for several high-order methods, as will be seen. 

V. Moureau, G. Lartigue, Y. Sommerer, C. Angelberger, O. Colin, and T. Poinsot. High-order methods for DNS and LES of compressible multi-component reacting flows on fixed and moving grids. J. Comput. Phys., 202(2) 710-736, 2005. 

T. E. Simos and Jesus Vigo-Aguiar, An exponentially-fitted high order method for longterm integration of periodic initial-value problems. Computer Physics Communications, 2001, 140, 358-365. 

T. E. Simos and J. Vigo-Aguiar, A symmetric high order method with minimal phase-lag for the numerical solution of the Schrodinger equation, International Journal of Modern Physics C, 2001(7), 1035-1042. 

Dorao CA (2006) High Order Methods for the Solution of the Population Balance Equation with Applications to Bubbly Flows. Dr ing thesis, Department of Chemical Engineering, The Norwegian University of Science and Technology, Trondheim... 

Demirdzic I, Lilek Z, Peric M (1993) A Collocated Finite Volume Method for Predicting Flows at all Speeds. Int J Numer Methods Fluids 16 1029-1050 Deville MO, Fischer PF, Mund EH (2002) High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge... 

E. Turkel, High-order methods, in Advances in Computational Electrodynamics The... 

Write out the update schemes Yoshida high-order methods of order 6 and 8. How many force evaluations are required per iteration ... 

Armero, F. Romero, I. 2001b. On the formulation of high-frequency dissipative timestepping algorithms for nonlinear dynamics. Part II High order methods . Comp. Meth. Appl. Mech. Eng., 190 6783-6824. 

The charge density index refers to the nature of the molecule before allowance is made for perturbing effects due to the approaching reactant. Such a method is often called a first-order method, a terminology that is discussed more fully in Chapter 12. For alternant molecules, it is necessary to proceed to a high-order method, one that reflects the ease with which molecular charge is drawn toward some atom, or pushed away from it, as approach by a charged chemical reactant makes that atom more or less attractive for electrons. An index which measures this is called atom self-polarizability, symbolized 7tr,r- The formulas for this and related polarizabilities are derived in Chapter 12. For now, we simply note that the formula is... 

Deville MO, Fischer PE, Mund EH (2002) High-order methods for incompressible fluid flow. Cambridge University Press, Cambridge... 

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