# Eigenmode Analysis of Boundary Conditions for the One-Dimensional Preconditioned Euler Equations

@article{Darmofal1999EigenmodeAO, title={Eigenmode Analysis of Boundary Conditions for the One-Dimensional Preconditioned Euler Equations}, author={David L. Darmofal and Pierre Moinier and Michael B. Giles}, journal={Journal of Computational Physics}, year={1999}, volume={160}, pages={369-384} }

The effect of local preconditioning on boundary conditions is analyzed for the subsonic, one-dimensional Euler equations. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions and different preconditioners whose intent is to accelerate low Mach number computations. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective when used with preconditioning, and asymptotically, at low…

## Tables from this paper

## 32 Citations

### Preconditioned characteristic boundary conditions for solution of the preconditioned Euler equations at low Mach number flows

- Computer ScienceJ. Comput. Phys.
- 2012

### Low-Mach preconditioned boundary conditions for compressible solvers

- Computer Science
- 2014

The theoretical development and application of preconditionsed impermeable boundaries in combination with preconditioned far-field conditions in the in-house CFD code TRACE is presented.

### Set of Boundary Conditions for Aerodynamic Design

- Engineering
- 2004

Robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well-posed problems. A boundary condition should be Robust and flexible numerical…

### Effects of condition number on preconditioning for low Mach number flows

- EngineeringJ. Comput. Phys.
- 2012

### Stable, Entropy-Pressure Compatible Subsonic Riemann Boundary Condition for Embedded Dg Compressible Flow Simulations

- EngineeringSSRN Electronic Journal
- 2022

One approach to reducing the computational cost of simulating transitional compressible boundary layer ﬂow is to adopt a near body reduced domain with boundary conditions enforced to be compatible…

### High-order Discontinuous Galerkin Solutions of Internal Low-mach Number Turbulent Flows☆

- Computer Science
- 2014

### Preconditioning of gas dynamics equations in compressible gas flow computations at low mach numbers

- Physics, Computer Science
- 2015

Features of the simulation of low-velocity inviscid and viscous compressible gas flows are considered, and a finite-volume discretization of gas dynamics equations at low Mach numbers on unstructured…

### High-order discontinuous Galerkin solutions of internal low-Mach number turbulent ﬂows

- Computer Science
- 2014

The method here presented is designed to improve the performance of the solution in the incompressible limit using an implicit scheme for the temporal integration of the compressible Reynolds Averaged Navier Stokes (RANS) equations.

### ON BOUNDARY CONDITIONS FOR MULTIDIMENSIONAL HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN THE FINITE VOLUME FRAMEWORK

- Mathematics, Computer Science
- 2002

This report presents a method for imposing boundary conditions in the context of hyperbolic systems of conservation laws in the finite volume framework and analytically and numerically compares the treatment with the incomplete Riemann invariant technique.

## References

SHOWING 1-10 OF 33 REFERENCES

### Eigenmode analysis of unsteady one-dimensional Euler equations

- Physics
- 1983

The initial boundary value problem describing the evolution of unsteady linearized perturbations of a steady, uniform subsonic flow is analyzed. The eigenmodes and eigenfrequencies of the system are…

### Characteristic time-stepping or local preconditioning of the Euler equations

- Computer Science
- 1991

A derivation is presented of a local preconditioning matrix for multidimensional Euler equations, that reduces the spread of the characteristic speeds to the lowest attainable value and is predicted to simplify convergence-acceleration boundary procedures.

### Preconditioning Methods for Low-Speed Flows.

- Mathematics
- 1996

We consider the steady-state equations for a compressible fluid. For low-speed flow, the system is stiff because the ratio of the convective speed to the speed of sound is quite small. To overcome…

### Preconditioned methods for solving the incompressible low speed compressible equations

- Mathematics, Computer Science
- 1987

### Analysis of a local matrix preconditioner for the 2-D Navier-Stokes equations

- Computer Science
- 1993

A local matrix preconditioner based on block-Jacobi is analyzed for the linearized 2-D compressible NavierStokes equations discretized using firstand secondorder accurate upwinding to tightly cluster residual eigenvalues for high-frequency Fourier modes.

### Preconditioning Applied to Variable and Constant Density Flows

- Computer Science
- 1995

A time-derivative preconditioning of the Navier-Stokes equations, suitable for both variable and constant density fluids, is developed and is shown to provide accurate steady-state solutions for transonic and low-speed flow of variable density fluids.

### Multi-stage schemes for the Euler and Navier-Stokes equations with optimal smoothing

- Computer Science
- 1993

The optimization technique is described, used to obtain the optimal sequence of time-step values for upwind Euler discretizations, and some convergence results for numerical integrations performed with the new schemes are presented.

### The application of preconditioning in viscous flows

- Computer Science
- 1993

A time-derivative preconditioning algorithm that is effective over a wide range of flow conditions from inviscid to very diffusive flows and from low speed to supersonic flows has been developed and convergence rates are shown to be accelerated by as much as two orders of magnitudes.

### Nonreflecting boundary conditions for Euler equation calculations

- Physics
- 1990

We present a unified theory for the construction of steady-state and unsteady nonreflecting boundary conditions for the Euler equations. These allow calculatios to be performed on truncated domains…