DEVELOPMENT OF A HIGHER-ORDER ACCURATE RECONSTRUCTION SCHEME WITH REDUCED LEAST SQUARE MATRIX FOR CONVECTIVE AND DIFFUSIVE FLUX EVALUATION

The development of a higher-order reconstruction scheme with reduced least square matrix is presented. The matrix used in conventional least square based reconstruction schemes for finite volume solvers contains bigger terms. For solution dependent schemes, this matrix has to be inverted for each time step, which is computationally costlier. To overcome this, certain mathematical principles applicable to finite volume formulation, have been used to eliminate a good number of terms appearing in the matrix. In addition, accurate and computationally efficient derivative plug-ins are incorporated to make the formulation generalized so that one can extend it to any order of accuracy. The presence of higher derivative terms in this scheme ensures uniformly higher-order accuracy throughout the flow domain. The reduced matrix can be used for data independent as well as solution dependent reconstruction schemes. Computationally efficient stencil searching algorithm, satisfying physical and topological requirements and capable of handling structured, unstructured, and adaptive grids has been coupled with the scheme. The scheme has been successfully used to simulate flow over blunt cone-flare, NASA B2 nozzle, and high altitude test facility. The solver has shown around 30% saving in least square matrix evaluation time.