Numerical Waves in High-Fidelity Simulations of Reacting Flows

2 Numerical Waves in High-Fidelity Simulations of Reacting Flows 

The main reason why numerical waves have not been discussed much in the CFD community is that most RANS codes use excessive artificial viscosity and large turbulent viscosity levels (due to turbulence models) which kills all numerical waves. They also kill all acoustic waves and all hydro-dynamic modes and cannot be used for the present needs of combustion research. Methods which can compute accurately waves in reacting flows must use centered schemes and LES (or DNS) formulations in order to avoid damping all waves (physical and numerical). A convenient way to illustrate this point is to compare the various viscosities pla3ung a role in a CFD code  

The first consequence of the introduction of two additional viscosities vt and Va to the true viscosity v is that the Reynolds number really seen by the code is  

Method Physical viscosity Numerical viscosity Turbulent viscosity Capacity to propagate waves 

A less pleasant implication of Table 8.2 is that, as soon as high-fidelity methods such as DNS or LES are developed, they have to avoid large values of turbulent and artificial viscosities. This requires small mesh sizes, high-order schemes, small time steps [268 362 340]. But even after all these improvements, these methods will remain sensitive to numerical waves [363]. In DNS or LES, numerical waves are intrinsic elements of the simulation and must be controlled by something other than viscosity. This usually means significant improvements of initial and boundary conditions and a careful 

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