Solution of the Euler equations on Cartesian grids

French, Ainslie D.

doi:10.1016/j.apnum.2003.12.014

Cited by 3 publications

(1 citation statement)

References 4 publications

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“…where ∆x l , ∆y l , ∆x m and ∆y m are given as [9,11,18]. These cell wise changes are appropriately distributed to cell vertices that make up the …”

Section: Fine Grid Solutionmentioning

confidence: 99%

Cell-Vertex Based Multigrid Solution of the Time-Domain Maxwell's Equations

Deore¹,

Chatterjee²

2010

PIER B

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Abstract-The time domain Maxwell's equations are numerically solved using a multigrid method in a scattered field formulation and a cell-vertex based finite volume time domain framework. The multilevel method is an adaptation of Ni's [9] cell-vertex based multigrid technique, proposed for accelerating steady state convergence of nonlinear Euler equations of gas dynamics. Accelerated convergence to steady state of the time domain Maxwell's equations, for problems involving electromagnetic scattering, is obtained using multiple grids without the use of additional numerical damping usually required in nonlinear problems. The linear nature of the Maxwell's system also allows for a more accurate representation of the fine-grid problem on the coarse grid.

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“…where ∆x l , ∆y l , ∆x m and ∆y m are given as [9,11,18]. These cell wise changes are appropriately distributed to cell vertices that make up the …”

Section: Fine Grid Solutionmentioning

confidence: 99%

Cell-Vertex Based Multigrid Solution of the Time-Domain Maxwell's Equations

Deore¹,

Chatterjee²

2010

PIER B

View full text Add to dashboard Cite

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Numerical Simulation of the Unsteady Aerodynamic Forces over a Circular Cylinder in Transonic Flow

Miserda

Leal

2006

44th AIAA Aerospace Sciences Meeting and Exhibit

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A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

Deore

Chatterjee²

2010

PIER M

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Abstract-A cell-vertex based finite volume scheme is used to solve the time-dependent Maxwell's equations and predict electromagnetic scattering from perfectly conducting bodies. The scheme is based on the cell-vertex finite volume integration method, originally proposed by Ni [1], for solution of the two dimensional unsteady Euler equations of gas dynamics. The resulting solution is second-order accurate in space and time, and requires cell based fluctuations to be appropriately distributed to the state vector stored at cell vertices at each time step. Results are presented for two-dimensional canonical shapes and complex three dimensional geometries. Unlike in gas dynamics, no user defined numerical damping is required in this novel cell-vertex based finite volume integration scheme when applied to the time-domain Maxwell's equations.

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Solution of the Euler equations on Cartesian grids

Cited by 3 publications

References 4 publications

Cell-Vertex Based Multigrid Solution of the Time-Domain Maxwell's Equations

Cell-Vertex Based Multigrid Solution of the Time-Domain Maxwell's Equations

Numerical Simulation of the Unsteady Aerodynamic Forces over a Circular Cylinder in Transonic Flow

A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

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