
doi: 10.2514/6.2004-740
A recently introduced global preconditioning technique is validated for the Euler equations. Energy and enthalpy equations are nondimensionalized by means of a reference enthalpy, resulting in increased numerical accuracy for low-speed flows. A cell-based, finite volume formulation is used, with flux dierence splitting and both explicit and implicit time integration schemes. A Newton-linearized iterative implicit algorithm is implemented, with Symmetric Gauss-Seidel(LU/SGS) nested sub-iterations. This choice eliminates approximate factorization errors, which become dominant at low speed flows. The linearized Jacobians are evaluated by numerical dierentiation. Higher-order discretization are constructed by means of the MUSCL approach. Locally one-dimensional Characteristic Variable Boundary Conditions are implemented at the farfield boundary. The preconditioned scheme is successfully applied to the following traditional test cases used as benchmarks for local preconditioning techniques: point disturbance, flow angle disturbance, and stagnation point arising from the impingement of two identical jets. The flow over a symmetric airfoil and a convergent-divergent nozzle are then simulated for arbitrary Mach numbers. The preconditioned scheme greatly enhances accuracy and convergence rate for low-speed flows (all the way down to M 10E 4). Some preliminary tests of fully unsteady flows are also conducted.
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