Mean-flow variables at the immersed boundary (IB) nodes (ie, interior near-wall nodes) are evaluated via linear interpolation in the normal direction to close the discrete form of governing equations. To reduce the near-wall mesh intervals, the tangential velocity at IB nodes is determined by enforcing the wall shear stress modified by the wall modeling technique. Analytical solutions in the near-wall region are utilized to determine the turbulence variables of SST k-ω or S-A model at IB nodes.

A wavelet-based adaptation methodology is proposed for hyperbolic conservation laws. The nonlinear weights of the conventional weighted essential nonoscillatory implementation are selectively modified to ensure lower dissipation. Scale-selective dissipation is dynamically provided at each level with a linear mapping function.