Y. Wang et al., A NONOSCILLATORY NO-FREE-PARAMETER FINITE-ELEMENT ALGORITHM AND ITS APPLICATIONS IN CFD, International journal for numerical methods in fluids, 24(2), 1997, pp. 141-153
A non-oscillatory no-free-parameter finite element method (NNFEM) is p
resented based on the consideration of wave propagation characteristic
in different characteristic directions across a strong discontinuity
through flux vector splitting in order to satisfy the increasing entro
py condition. The algorithm is analysed in detail for the one-dimensio
nal (1D) Euler equation and then extended to the 2D, axisymmetric and
3D Euler and Navier-Stokes equations. Its applications in various case
s-inviscid oblique shock wave reflection, flow over a forward step, ax
isymmetric free jet flow, supersonic flows over 2D and 3D rectangular
cavities-are given. These computational results show that the present
NNFEM is efficient in practice and stable in operations and is especia
lly capable of giving good resolution in simulating complicated separa
ted and vortical flows interacting with shock waves.