Subgrid modelling studies with Burgers’ equation

Burgers’ equation, a one-dimensional analogue of the Navier–Stokes equation, has been solved numerically in full detail at high (equivalent) Reynolds numbers. These fine-mesh solutions have been used to study the dynamics of the Burgers’ equation analogue of three-dimensional turbulence and in particular the drain of energy from the large to the small structures. The equation has also been solved on a coarse mesh, using various forms of subgrid model. The solutions so derived have been compared with filtered solutions of the same problem on a fine mesh. In this way it has been possible to test directly the performance of subgrid models at high Reynolds numbers, a test which cannot be made on the Navier–Stokes equations themselves. With proper choice of the parameters, the performance of the subgrid models is very satisfactory.