A CFD Euler solver from a physical acoustics–convection flux Jacobian decomposition
| Autor: | Joe Iannelli |
|---|---|
| Rok vydání: | 1999 |
| Předmět: |
Discretization
Differential equation business.industry Applied Mathematics Mechanical Engineering Mathematical analysis Computational Mechanics Geometry Upwind scheme Computational fluid dynamics Finite element method Computer Science Applications Euler equations Runge–Kutta methods symbols.namesake Mechanics of Materials Euler's formula symbols business Mathematics |
| Zdroj: | International Journal for Numerical Methods in Fluids. 31:821-860 |
| ISSN: | 1097-0363 0271-2091 |
| DOI: | 10.1002/(sici)1097-0363(19991115)31:5<821::aid-fld899>3.0.co;2-# |
| Popis: | We introduce a continuum, i.e. non-discrete, upstream-bias formulation that rests on the physics and mathematics of acoustics and convection. The formulation induces the upstream-bias at the differential equation level, within a characteristics-bias system associated with the Euler equations with general equilibrium equations of state. For low subsonic Mach numbers, this formulation returns a consistent upstream-bias approximation for the non-linear acoustics equations. For supersonic Mach numbers, the formulation smoothly becomes an upstream-bias approximation of the entire Euler flux. With the objective of minimizing induced artificial diffusion, the formulation non-linearly induces upstream-bias, essentially locally, in regions of solution discontinuities, whereas it decreases the upstream-bias in regions of solution smoothness. The discrete equations originate from a finite element discretization of the characteristic-bias system and are integrated in time within a compact block tridiagonal matrix statement by way of an implicit non-linearly stable Runge-Kutta algorithm for stiff systems |
| Databáze: | OpenAIRE |
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