本研究運用計算流體力學（Computational Fluid Dynamics, CFD）技術，採用直接數值模擬（Direct Numerical Simulation, DNS）方法，針對根管治療中正壓灌洗的流場行為進行高解析度模擬，系統性探討針頭尺寸、插入位置、傾斜角度與出口速度等操作參數對灌洗效率與灌洗範圍的影響。
模擬模型採用具臨床代表性的中空錐形根管幾何，灌洗液為水，構建三維可壓縮流場求解架構。為兼顧幾何邊界的精確處理與高效數值收斂，本研究結合 Build-ing Cube Method（BCM）與沉浸邊界法（Immersed Boundary Method, IBM）進行階層式正交網格劃分與固壁處理，並搭配全域統一解法、Roe 數值通量計算與 LUSGS 隱式時間積分法，以實現可壓縮低速流場的直接求解。
模擬設計涵蓋 25G 與 30G 開口式針頭，搭配多組流速、插入深度與傾斜角度參數條件，觀察其對流速場、壁面剪應力與根尖壓力分佈的影響。結果顯示，針頭與根管壁間隙為影響剪應力集中區位置的關鍵因子，當間隙縮小時將導致局部流速梯度與剪應力顯著上升，強化針頭周圍區域的清潔能力；反之，若欲擴展灌洗範圍，則應選用細口徑針頭並調整插入位置以延伸流體推進距離。
此外，提升出口流速雖可提高剪應力強度，但同時顯著增加根尖壓力，需在提高清潔效率與避免液體外滲間取得平衡。針頭傾斜角則會導致局部流場不對稱與單側剪應力增強，但對灌洗深度的影響相對有限。
整體而言，本研究開發之高解析度數值模擬架構可準確呈現不同臨床操作參數對灌洗行為的影響，並量化關鍵效能指標，如剪應力與灌洗範圍位置，具臨床應用價值。未來可進一步延伸至聲波或超音波灌洗等高階灌洗技術之模擬分析，作為臨床技術優化與針具設計的重要參考依據。

This study employs Computational Fluid Dynamics (CFD) with a Direct Numerical Simulation (DNS) approach to investigate the fluid behavior of positive-pressure irrigation in root canal treatment. A high-resolution three-dimensional compressible flow model is con-structed to systematically examine the effects of needle gauge, insertion depth, inclination angle, and outlet velocity on irrigation efficiency and spatial coverage.
A clinically representative hollow conical root canal geometry is used, with water modeled as the irrigant. To accurately capture complex boundaries and ensure computational efficiency, a combination of the Building Cube Method (BCM) and the Immersed Boundary Method (IBM) is applied for hierarchical orthogonal mesh generation and wall treatment. The compressible Navier–Stokes equations are solved using a unified solution strategy incorporating Roe's scheme and an implicit Lower–Upper Symmetric Gauss–Seidel (LUSGS) time integration method, enabling direct resolution of the flow field without turbulence modeling.

While increasing flow velocity boosts shear stress, it also significantly elevates apical pres-sure, which may raise the risk of irrigant extrusion. Needle inclination introduces flow asymmetry and enhances shear stress on one canal wall, but shows limited influence on irrigant penetration depth.
Overall, the proposed high-fidelity simulation framework effectively captures the influence of clinically relevant needle parameters on root canal irrigation behavior. By quantifying key performance metrics such as shear stress intensity and irrigant reach, the findings pro-vide practical guidance for optimizing irrigation protocols and needle design. This model can be further extended to simulate sonic or ultrasonic irrigation scenarios for comprehen-sive evaluation of advanced endodontic techniques.

[1] H. Schilder, "Cleaning and shaping the root canal," Dental clinics of north America, vol. 18, no. 2, pp. 269-296, 1974.
[2] M. Haapasalo, Y. Shen, W. Qian, and Y. Gao, "Irrigation in endodontics," Dental Clinics, vol. 54, no. 2, pp. 291-312, 2010.
[3] M. Abou-Rass and M. V. Piccinino, "The effectiveness of four clinical irrigation methods on the removal of root canal debris," Oral surgery, oral medicine, oral pathology, vol. 54, no. 3, pp. 323-328, 1982.
[4] L. J. Albrecht, J. C. Baumgartner, and J. G. Marshall, "Evaluation of apical debris removal using various sizes and tapers of ProFile GT files," Journal of endodontics, vol. 30, no. 6, pp. 425-428, 2004.
[5] Y. Gao et al., "Development and validation of a three-dimensional computational fluid dynamics model of root canal irrigation," Journal of Endodontics, vol. 35, no. 9, pp. 1282-1287, 2009.
[6] C. Boutsioukis et al., "The effect of needle-insertion depth on the irrigant flow in the root canal: evaluation using an unsteady computational fluid dynamics model," Journal of endodontics, vol. 36, no. 10, pp. 1664-1668, 2010.
[7] K. W. Falk and C. M. Sedgley, "The influence of preparation size on the mechanical efficacy of root canal irrigation in vitro," Journal of endodontics, vol. 31, no. 10, pp. 742-745, 2005.
[8] J. E. Chen, B. Nurbakhsh, G. Layton, M. Bussmann, and A. Kishen, "Irrigation dynamics associated with positive pressure, apical negative pressure and passive ultrasonic irrigations: a computational fluid dynamics analysis," Australian Endodontic Journal, vol. 40, no. 2, pp. 54-60, 2014.
[9] T. Y. Huang, K. Gulabivala, and Y. L. Ng, "A bio‐molecular film ex‐vivo model to evaluate the influence of canal dimensions and irrigation variables on the efficacy of irrigation," International endodontic journal, vol. 41, no. 1, pp. 60-71, 2008.
[10] C. Boutsioukis, C. Gogos, B. Verhaagen, M. Versluis, E. Kastrinakis, and L. Van der Sluis, "The effect of apical preparation size on irrigant flow in root canals evaluated using an unsteady Computational Fluid Dynamics model," International endodontic journal, vol. 43, no. 10, pp. 874-881, 2010.
[11] C. Boutsioukis, C. Gogos, B. Verhaagen, M. Versluis, E. Kastrinakis, and L. Van der Sluis, "The effect of root canal taper on the irrigant flow: evaluation using an unsteady Computational Fluid Dynamics model," International endodontic journal, vol. 43, no. 10, pp. 909-916, 2010.
[12] M. Ghalandari, E. Mirzadeh Koohshahi, F. Mohamadian, S. Shamshirband, and K. W. Chau, "Numerical simulation of nanofluid flow inside a root canal," Engineering Applications of Computational Fluid Mechanics, vol. 13, no. 1, pp. 254-264, 2019.
[13] W. S. Fu, C. G. Li, W. F. Lin, and Y. H. Chen, "Roe scheme with preconditioning method for large eddy simulation of compressible turbulent channel flow," International journal for numerical methods in fluids, vol. 61, no. 8, pp. 888-910, 2009.
[14] W.-S. Fu, C.-G. Li, C.-P. Huang, and J.-C. Huang, "An investigation of a high temperature difference natural convection in a finite length channel without Bossinesq assumption," International journal of heat and mass transfer, vol. 52, no. 11-12, pp. 2571-2580, 2009.
[15] C.-G. Li, M. Tsubokura, and K. Onishi, "Feasibility investigation of compressible direct numerical simulation with a preconditioning method at extremely low Mach numbers," International Journal of Computational Fluid Dynamics, vol. 28, no. 6-10, pp. 411-419, 2014.
[16] C. H. Cooke and T. J. Chen, "On shock capturing for pure water with general equation of state," Communications in applied numerical methods, vol. 8, no. 4, pp. 219-233, 1992.
[17] K. Nakahashi and L. Kim, "Building-cube method for large-scale, high resolution flow computations," in 42nd AIAA aerospace sciences meeting and exhibit, 2004, p. 434.
[18] K. Komatsu et al., "Parallel processing of the Building-Cube Method on a GPU platform," Computers & Fluids, vol. 45, no. 1, pp. 122-128, 2011.
[19] M. D. de Tullio, P. De Palma, G. Iaccarino, G. Pascazio, and M. Napolitano, "An immersed boundary method for compressible flows using local grid refinement," Journal of Computational Physics, vol. 225, no. 2, pp. 2098-2117, 2007.
[20] R. Ghias, R. Mittal, and H. Dong, "A sharp interface immersed boundary method for compressible viscous flows," Journal of Computational Physics, vol. 225, no. 1, pp. 528-553, 2007.
[21] C.-G. Li, R. Bale, W. Wang, and M. Tsubokura, "A sharp interface immersed boundary method for thin-walled geometries in viscous compressible flows," International Journal of Mechanical Sciences, vol. 253, p. 108401, 2023.
[22] C.-G. Li, M. Tsubokura, and R. Bale, "Framework for simulation of natural convection in practical applications," International Communications in Heat and Mass Transfer, vol. 75, pp. 52-58, 2016.
[23] P. L. Roe, "Approximate Riemann solvers, parameter vectors, and difference schemes," Journal of computational physics, vol. 43, no. 2, pp. 357-372, 1981.
[24] J. M. Weiss and W. A. Smith, "Preconditioning applied to variable and constant density flows," AIAA journal, vol. 33, no. 11, pp. 2050-2057, 1995.
[25] C.-G. Li, "A compressible solver for the laminar–turbulent transition in natural convection with high temperature differences using implicit large eddy simulation," International Communications in Heat and Mass Transfer, vol. 117, p. 104721, 2020.
[26] B. Ren, C.-G. Li, and M. Tsubokura, "Direct numerical simulation of vertically heated natural convection over 3D irregular roughness," Computers & Fluids, vol. 257, p. 105866, 2023.
[27] B. Ren, C.-G. Li, and M. Tsubokura, "The effects of irregular roughness with different surface power spectrums on the heat transfer of natural convection in enclosures," International Communications in Heat and Mass Transfer, vol. 141, p. 106581, 2023.
[28] S. Yoon and A. Jameson, "Lower-upper symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations," AIAA journal, vol. 26, no. 9, pp. 1025-1026, 1988.
[29] G. V. Candler, M. J. Wright, and J. D. McDonald, "Data-parallel lower-upper relaxation method for reacting flows," AIAA journal, vol. 32, no. 12, pp. 2380-2386, 1994.
[30] K. Gulabivala, Y. Ng, M. Gilbertson, and I. Eames, "The fluid mechanics of root canal irrigation," Physiological measurement, vol. 31, no. 12, p. R49, 2010.