3D finite-difference dynamic-rupture modeling along nonplanar faults

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM123-SM137 ◽  
Author(s):  
Víctor M. Cruz-Atienza ◽  
Jean Virieux ◽  
Hideo Aochi
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Heterogeneous Media ◽  
Slip Rate ◽  
Quantitative Agreement ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Weight Functions ◽  
Dynamic Rupture ◽  
Fault Surface

Proper understanding of seismic emissions associated with the growth of complexly shaped microearthquake networks and larger-scale nonplanar fault ruptures, both in arbitrarily heterogeneous media, requires accurate modeling of the underlying dynamic processes. We present a new 3D dynamic-rupture, finite-difference model called the finite-difference, fault-element (FDFE) method; it simulates the dynamic rupture of nonplanar faults subjected to regional loads in complex media. FDFE is based on a 3D methodology for applying dynamic-rupture boundary conditions along the fault surface. The fault is discretized by a set of parallelepiped fault elements in which specific boundary conditions are applied. These conditions are applied to the stress tensor, once transformed into a local fault referenceframe. Numerically determined weight functions multiplying particle velocities around each element allow accurate estimates of fault kinematic parameters (i.e., slip and slip rate) independent of faulting mechanism. Assuming a Coulomb-like slip-weakening friction law, a parametric study suggests that the FDFE method converges toward a unique solution, provided that the cohesive zone behind the rupture front is well resolved (i.e., four or more elements inside this zone). Solutions are free of relevant numerical artifacts for grid sizes smaller than approximately [Formula: see text]. Results yielded by the FDFE approach are in good quantitative agreement with those obtained by a semianalytical boundary integral method along planar and nonplanar parabola-shaped faults. The FDFE method thus provides quantitative, accurate results for spontaneous-rupture simulations on intricate fault geometries.

A Multipole Accelerated Desingularized Method for Computing Nonlinear Wave Forces on Bodies

1998 ◽  
Vol 120 (2) ◽  
pp. 71-76 ◽  
Author(s):  
S. M. Scorpio ◽  
R. F. Beck
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Mixed Boundary ◽  
Offshore Structures ◽  
Computational Effort ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Wave Forces ◽  
Surface Boundary ◽  
Time Step

Nonlinear wave forces on offshore structures are investigated. The fluid motion is computed using a Euler-Lagrange time-domain approach. Nonlinear free surface boundary conditions are stepped forward in time using an accurate and stable integration technique. The field equation with mixed boundary conditions that result at each time step are solved at N nodes using a desingularized boundary integral method with multipole acceleration. Multipole accelerated solutions require O(N) computational effort and computer storage, while conventional solvers require O(N2) effort and storage for an iterative solution and O(N3) effort for direct inversion of the influence matrix. These methods are applied to the three-dimensional problem of wave diffraction by a vertical cylinder.

Properties of Finite-Difference Operators for the Steady-Wave Problem

1993 ◽  
Vol 37 (01) ◽  
pp. 1-7
Author(s):  
John S. Letcher
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Radiation Condition ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Difference Operators ◽  
Surface Boundary ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

A feature of most implementations of Dawson's boundary-integral method for steady free-surface flows is the use of upstream finite-difference operators for the streamwise derivative occurring in the linearized free-surface boundary condition. An algebraic analysis of a family of candidate operators reveals their essential damping and dispersion error characteristics, which correlate well with their observed performance in two-dimensional example flows. Some new operators are found which perform somewhat better than Dawson's, but the general outlook for accurate results using difference operators is nevertheless bleak. It is shown that the calculation necessarily diverges as panel size is reduced, and a breakdown at higher speeds is also inevitable. More promise appears to lie in satisfying the radiation condition by several alternative ways, which are briefly discussed.

Investigation on the Dynamic Rupture of the 1970 Ms 7.7 Tonghai, Yunnan, China, Earthquake on the Qujiang Fault

2020 ◽  
Vol 110 (2) ◽  
pp. 898-919
Author(s):  
Houyun Yu ◽  
Wenqiang Zhang ◽  
Zhenguo Zhang ◽  
Zhengbo Li ◽  
Xiaofei Chen
Keyword(s):  
Heterogeneous Media ◽  
Velocity Structure ◽  
Maximum Principal Stress ◽  
Seismic Intensity ◽  
Fault Model ◽  
Dynamic Rupture ◽  
Low Velocity ◽  
Regional Stress ◽  
Fault Surface ◽  
Earthquake Scenarios

ABSTRACT Regional stress states and fault geometries play important roles in earthquake rupture dynamics. Using the curved grid finite-difference method, we conducted 3D spontaneous rupture simulations of the nonplanar Qujiang fault (QF) to investigate the rupture processes of the 1970 Tonghai earthquake and potential future earthquakes. A nonplanar fault model including topography was adopted and embedded in heterogeneous media. Regional stress orientations with an interval of 5° were tested, and various fault geometry models with different fault surface traces and fault dips were discussed. We also provided explanations for the unbroken northwestern segment of the QF and the seismic intensity anomaly in the Tonghai basin during the 1970 Tonghai event. Finally, we presented several future potential earthquake scenarios occurring on the QF at three nucleation locations. Our simulation results suggested that the maximum principal stress azimuth around the Tonghai area is N25°W and that the QF is most likely a complex dipping fault—the southeastern segment dips to the northeast, whereas the northwestern segment dips to the southwest. Our simulations also revealed that multiple explanations, including a regional stress rotation and an increase in the cohesion force, could account for the unbroken northwestern segment of the QF. Furthermore, the seismic intensity anomaly in the Tonghai basin can be explained by a low-velocity structure. Future earthquake scenarios demonstrated that potential earthquakes nucleating at Eshan and Wujie in a complex dipping fault model could rupture the entire QF, thereby posing severe seismic risks to nearby regions. In contrast, when the nucleation point was located at Quxi, the rupture was constrained to the initial fault segment of the QF; however, caution should still be exercised in the Quxi area because this scenario produces a maximum intensity of VIII.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

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