Finite-difference method-of-characteristics scheme for the equationsof gasdynamics

Parpia, Ijaz H.

doi:10.2514/3.10621

Cited by 3 publications

(6 citation statements)

References 17 publications

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“…It is worthwhile observing, in particular, that the dependent variables p and u are differentiated along two distinct directions, both lying on the same characteristic surface, as is expected when using nonorthogonal reference frames [29]. Conversely, in the case a (uniform) orthonormal reference frame is used, and n coincide (cf.…”

Section: A Transverse Terms From Different Perspectivementioning

confidence: 94%

“…(42) is identically zero as well ( i i i i 0 in Eq. (29) in the three-dimensional case), thus making the two formulations actually equivalent.…”

Section: A Gaussian Vortex Testmentioning

confidence: 95%

“…(24)(25)(26)(27)(28)(29), it is readily verified that the sum @W=@t L L t makes up the material derivatives of the dependent variables along the above-defined directions. In particular, Eq.…”

Section: A Transverse Terms From Different Perspectivementioning

confidence: 98%

“…Splitting T 1 as T 1 L t1 , these two terms being obtained from Eqs. (29) and (30) written in Cartesian coordinates, and using different relaxation coefficients, the boundary condition for L 1 becomes…”

Section: A Transverse Terms From Different Perspectivementioning

confidence: 99%

“…(15), the characteristic problem is analyzed under a more general perspective, i.e., the characteristic problem is reformulated in the most general case of a nonorthogonal rotated reference frame (see [29][30][31] for details on the use of generalized coordinates in the characteristic equations). In the transformed system, the different contributions to the transverse terms in the boundary conditions will be analyzed.…”

Section: A Transverse Terms From Different Perspectivementioning

confidence: 99%

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Optimal Inclusion of Transverse Effects in the NonReflecting Outflow Boundary Condition

2012

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The inclusion of transverse effects in designing characteristic boundary conditions for the Euler and NavierStokes equations was discussed by different authors and has proved to give some improvement in the perspective of reducing numerical perturbations generated at open boundaries. Based on the most general characteristic formulation using nonorthogonal and rotated reference frames, an analysis of the different terms involved in such an approach is carried out in the present work. To achieve the best performance for the numerical behavior of the boundary condition, it is then shown that different transverse terms need to be treated differently when included in the definition of the incoming wave amplitude variations. The analysis is supported by a series of numerical tests involving an inviscid vortex convected at an angle or a purely acoustic wave propagating radially. It is concluded that the optimal behavior in terms of acoustic reflection by outgoing vorticity can be achieved by minimizing the contribution of the transverse terms related to the material derivatives along the bicharacteristics, either by properly relaxing them or by selecting a characteristic direction which is not necessarily orthogonal to the boundary. Nomenclature= specific total energy (thermal kinetic), m 2 =s 2 E glb ; t = normalized global error for quantity F i = i-th component of the conservative flux vector-tensor J = Jacobian of the transformation between global and local generalized components j = 1 p , imaginary constant K = pressure relaxation coefficient, m 2 =kg L = reference length scale, m L = vector of the characteristic wave amplitude variations L t = generalized transverse propagation terms l, k = wavenumbers, 1=m M, M 1 = Mach number, reference Mach number n, t, k = basis of the local nonorthogonal reference frame p, p 1 = pressure and reference outlet pressure, respectively, Pa P = Jacobian of the transformation between conservative and primitive variables q = u i u i , m 2 =s 2 R v = vortex radius, m R = matrix of reflection coefficients S 1 , S = matrix of the right eigenvectors of A 1 and A , respectively s = entropy mode connected characteristic variable T = vector of transverse terms T = generalized transverse coupling terms t = time, s U, U = vectors of conservative and primitive variables, respectively u i , u 1 = i-th component of the velocity vector and reference velocity, respectively, m=s W = characteristic variables vector x i = i-th component of the position vector, m x 0 , y 0 = initial location of the vortex center, m ,= a dimensional pressure relaxation coefficients l , t = transverse relaxation coefficients = specific heat capacities ratio ij = Kronecker delta function " ijk = Levi-Civita symbol = base flow angle , = diagonal matrix of the eigenvalues of A 1 and A , respectively , , = local nonorthogonal reciprocal basis = eigenvalue of the nonconservative Jacobian, m=s, or reciprocal phase velocity, s=m i = i = j j 1=2 , , = coordinates in the local nonorthogonal reference frame (m) , 1 = density and ...

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Section: A Transverse Terms From Different Perspectivementioning

confidence: 94%

“…(42) is identically zero as well ( i i i i 0 in Eq. (29) in the three-dimensional case), thus making the two formulations actually equivalent.…”

Section: A Gaussian Vortex Testmentioning

confidence: 95%

Section: A Transverse Terms From Different Perspectivementioning

confidence: 98%

Section: A Transverse Terms From Different Perspectivementioning

confidence: 99%

Section: A Transverse Terms From Different Perspectivementioning

confidence: 99%

See 3 more Smart Citations

Optimal Inclusion of Transverse Effects in the NonReflecting Outflow Boundary Condition

2012

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Genuinely multidimensional characteristic‐based scheme for incompressible flows

Razavi

Zamzamian

Farzadi

2007

Numerical Methods in Fluids

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SUMMARYThis paper presents a novel multidimensional characteristic-based (MCB) upwind method for the solution of incompressible Navier-Stokes equations. As opposed to the conventional characteristic-based (CB) schemes, it is genuinely multidimensional in that the local characteristic paths, along which information is propagated, are used. For the first time, the multidimensional characteristic structure of incompressible flows modified by artificial compressibility is extracted and used to construct an inherent multidimensional upwind scheme. The new proposed MCB scheme in conjunction with the finite-volume discretization is employed to model the convective fluxes. Using this formulation, the steady two-dimensional incompressible flow in a lid-driven cavity is solved for a wide range of Reynolds numbers. It was found that the new proposed scheme presents more accurate results than the conventional CB scheme in both their firstand second-order counterparts in the case of cavity flow. Also, results obtained with second-order MCB scheme in some cases are more accurate than the central scheme that in turn provides exact second-order discretization in this grid. With this inherent upwinding technique for evaluating convective fluxes at cell interfaces, no artificial viscosity is required even at high Reynolds numbers. Another remarkable advantage of MCB scheme lies in its faster convergence rate with respect to the CB scheme that is found to exhibit substantial delays in convergence reported in the literature. The results obtained using new proposed scheme are in good agreement with the standard benchmark solutions in the literature.

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Multi-Dimensional Semi-Lagrangian Characteristic Approach to the Shallow Water Equations by the Cip Method

Ogata¹,

Yabe²

2004

Int. J. Comp. Eng. Sci.

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Finite-difference method-of-characteristics scheme for the equationsof gasdynamics

Cited by 3 publications

References 17 publications

Optimal Inclusion of Transverse Effects in the NonReflecting Outflow Boundary Condition

Optimal Inclusion of Transverse Effects in the NonReflecting Outflow Boundary Condition

Genuinely multidimensional characteristic‐based scheme for incompressible flows

Multi-Dimensional Semi-Lagrangian Characteristic Approach to the Shallow Water Equations by the Cip Method

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