袁禮++張文生

摘 要：泥石流/滑坡碎屑流等地質(zhì)災(zāi)害的沖擊力和泛濫范圍可用顆粒流薄層模型進(jìn)行數(shù)值模擬研究。探索地質(zhì)體內(nèi)部結(jié)構(gòu)可用波場(chǎng)探測(cè)方法。該研究給出了面向以上兩方面計(jì)算問(wèn)題的階段性工作。針對(duì)顆粒流薄層近似模型Savage-Hutter方程，我們應(yīng)用無(wú)振蕩中心（NOC）格式和結(jié)合MUSCL重構(gòu)的LF格式，以及GPU-CUDA并行計(jì)算技術(shù)求解此方程。為了準(zhǔn)確地模擬顆粒所受的實(shí)際摩擦力，計(jì)算中采用了靜力學(xué)條件和停止準(zhǔn)則。還將靜力學(xué)條件和停止準(zhǔn)則引入開(kāi)源軟件titan2d中。通過(guò)數(shù)值模擬幾個(gè)簡(jiǎn)單問(wèn)題，給出了NOC格式和LF-MUSCL格式的計(jì)算精度、效率和復(fù)雜程度的比較；通過(guò)對(duì)武隆滑坡和舟曲泥石流問(wèn)題的模擬，顯示了軟件titan2d計(jì)算結(jié)果的合理性，表明該軟件值得進(jìn)一步發(fā)展。求解多孔介質(zhì)彈性波方程在地質(zhì)力學(xué)和地球物理領(lǐng)域中有重要應(yīng)用價(jià)值，在實(shí)際計(jì)算時(shí)都必須要引入吸收邊界條件，否則會(huì)影響波場(chǎng)傳播的精度。該研究首次推導(dǎo)得到了三維多孔介質(zhì)彈性波傳播的精確的吸收邊界條件。該條件由6個(gè)復(fù)雜的方程組成，而且空間是非局部的，時(shí)間是局部的，可以用標(biāo)準(zhǔn)的數(shù)值方法如有限元和有限差分法等進(jìn)行計(jì)算。該結(jié)果有直接和潛在的應(yīng)用價(jià)值。

關(guān)鍵詞：NOC格式 有限體積法 GPU-CUDA計(jì)算 TITAN2D軟件 多空介質(zhì)彈性波 無(wú)反射邊界條件

Numerical Schemes for the Savage-Hutter Equations for Granular Flows and Exact Absorbing Boundary Conditions for wave Propagation in 3D Porous Media

Yuan Li Zhang Wensheng

（Institute of Mathematics and Systems Science， Chinese Academy of Sciences）

Abstract：The impact intensities and influencing areas of debris flows in geological disasters can be simulated numerically by using thin layer models for granular flows. Interior compositions and structures below the earth surface can be explored by using wave detection methods. This report gives periodical progress towards solving the above two computational issues. For numerical solution of the Savage-Hutter equations， we apply the Non-Oscillatory Central （NOC） scheme and the LF scheme in conjunction with the MUSCL reconstruction for primitive variables， as well as GPU-CUDA parallel computing technology. Static resistance conditions and stopping criteria are implemented in order to accurately compute the friction force. They are also inserted into the open source code TITAN2D. Numerical tests against several typical examples compare the accuracy， efficiency and easiness to use between the two numerical schemes. Numerical simulations of Wulong landslide and Zhouqu debris flow disasters by using the code TITAN2D demonstrate that the numerical results are reasonable， and the code is worthy of further development. Solving the poroelastic wave equations has important application values in the area of geomechanics and geophysics. In practical computations the absorbing boundary conditions are required to increase the computational accuracy of wave propagation. We for the first time derive and obtain the exact nonreflecting boundary conditions for three dimensional poroelastic wave equations. The conditions are composed of six complicate equations and are nonlocal in space but local in time， thus they can be computed numerically with standard methods such as the finite-difference method and finite-element method. The result has direct and potential application values.

Key Words：NOC scheme； Finite volume method； GPU-CUDA computing； TITAN2D code；Poroelastic wave； Nonreflecting boundary condition