Assessment of thermal discomfortin non-uniformly heated enclosures: Two indices in the time-space domain

1994 ◽  
Vol 18 (8) ◽  
pp. 701-710
Author(s):  
G. Cammarata ◽  
A. Fichera ◽  
L. Marletta
Keyword(s):  
Space Domain ◽  
Time Space ◽  
Two Indices

Time-space-domain implicit finite-difference methods for modeling acoustic wave equations

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. T175-T193 ◽  
Author(s):  
Enjiang Wang ◽  
Jing Ba ◽  
Yang Liu
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Wave Equations ◽  
Finite Difference Methods ◽  
Second Order ◽  
Computational Time ◽  
Time Step ◽  
Space Domain ◽  
Time Space ◽  
Temporal Dispersion

It has been proved that the implicit spatial finite-difference (FD) method can obtain higher accuracy than explicit FD by using an even smaller operator length. However, when only second-order FD in time is used, the combined FD scheme is prone to temporal dispersion and easily becomes unstable when a relatively large time step is used. The time-space domain FD can suppress the temporal dispersion. However, because the spatial derivatives are solved explicitly, the method suffers from spatial dispersion and a large spatial operator length has to be adopted. We have developed two effective time-space-domain implicit FD methods for modeling 2D and 3D acoustic wave equations. First, the high-order FD is incorporated into the discretization for the second-order temporal derivative, and it is combined with the implicit spatial FD. The plane-wave analysis method is used to derive the time-space-domain dispersion relations, and two novel methods are proposed to determine the spatial and temporal FD coefficients in the joint time-space domain. First, we fix the implicit spatial FD coefficients and derive the quadratic convex objective function with respect to temporal FD coefficients. The optimal temporal FD coefficients are obtained by using the linear least-squares method. After obtaining the temporal FD coefficients, the SolvOpt nonlinear algorithm is applied to solve the nonquadratic optimization problem and obtain the optimized temporal and spatial FD coefficients simultaneously. The dispersion analysis, stability analysis, and modeling examples validate that the proposed schemes effectively increase the modeling accuracy and improve the stability conditions of the traditional implicit schemes. The computational efficiency is increased because the schemes can adopt larger time steps with little loss of spatial accuracy. To reduce the memory requirement and computational time for storing and calculating the FD coefficients, we have developed the representative velocity strategy, which only computes and stores the FD coefficients at several selected velocities. The modeling result of the 2D complicated model proves that the representative velocity strategy effectively reduces the memory requirements and computational time without decreasing the accuracy significantly when a proper velocity interval is used.

Acoustic and elastic modeling by optimal time-space-domain staggered-grid finite-difference schemes

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T17-T40 ◽  
Author(s):  
Zhiming Ren ◽  
Yang Liu
Keyword(s):  
Finite Difference ◽  
Stability Condition ◽  
Computational Cost ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Equation Modeling ◽  
Optimal Time ◽  
Finite Difference Schemes ◽  
Space Domain ◽  
Time Space

Staggered-grid finite-difference (SFD) methods are widely used in modeling seismic-wave propagation, and the coefficients of finite-difference (FD) operators can be estimated by minimizing dispersion errors using Taylor-series expansion (TE) or optimization. We developed novel optimal time-space-domain SFD schemes for acoustic- and elastic-wave-equation modeling. In our schemes, a fourth-order multiextreme value objective function with respect to FD coefficients was involved. To yield the globally optimal solution with low computational cost, we first used variable substitution to turn our optimization problem into a quadratic convex one and then used least-squares (LS) to derive the optimal SFD coefficients by minimizing the relative error of time-space-domain dispersion relations over a given frequency range. To ensure the robustness of our schemes, a constraint condition was imposed that the dispersion error at each frequency point did not exceed a given threshold. Moreover, the hybrid absorbing boundary condition was applied to remove artificial boundary reflections. We compared our optimal SFD with the conventional, TE-based time-space-domain, and LS-based SFD schemes. Dispersion analysis and numerical simulation results suggested that the new SFD schemes had a smaller numerical dispersion than the other three schemes when the same operator lengths were adopted. In addition, our LS-based time-space-domain SFD can obtain the same modeling accuracy with shorter spatial operator lengths. We also derived the stability condition of our schemes. The experiment results revealed that our new LS-based SFD schemes needed a slightly stricter stability condition.

Acoustic Wave Equation Modeling with New Time-Space Domain Finite Difference Operators

2013 ◽  
Vol 56 (6) ◽  
pp. 840-850 ◽  
Author(s):  
LIANG Wen-Quan ◽  
YANG Chang-Chun ◽  
WANG Yan-Fei ◽  
LIU Hong-Wei
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Equation Modeling ◽  
Difference Operators ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
Time Space ◽  
New Time
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