An accurate and efficient gridless method based on implicit, fast, and constrained weights optimization schemes for compressible flows

An accurate and efficient gridless method is presented for calculation of inviscid compressible flows in subsonic to supersonic flows. The Taylor series least squares is used for discretization of spatial derivatives at each point. Fast gridless method using the second- and fourth-order artificial dissipation terms is applied for solving the Euler equations. Two methods are proposed for increasing the accuracy; implementing the constrained weights optimization and using high-order Taylor series expansion on the fast gridless method. The explicit and implicit dual-time schemes are applied for temporal discretization. To speed up convergence, local time stepping and residual smoothing techniques are used. The capability and accuracy of the methods are compared with other gridless methods, finite volume method and AGARD data for some test cases in subsonic, transonic and supersonic flows. Results show that the use of the constraint weights optimization increases the accuracy especially with fewer point distributions in comparison with conventional gridless methods and it is more efficient than other gridless methods.