scholarly journals A direct method for evaluating arbitrary high-order singular curved boundary integrals

2013 ◽  
Author(s):  
Xiaowei Gao ◽  
Weizhe Feng ◽  
Jinjun Zhao ◽  
Miao Cui
Keyword(s):  
Direct Method ◽  
High Order ◽  
Boundary Integrals ◽  
Curved Boundary ◽  
A Direct Method

scholarly journals High Order Projection Plane Method for Evaluation of Supersingular Curved Boundary Integrals in BEM

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Miao Cui ◽  
Wei-zhe Feng ◽  
Xiao-wei Gao ◽  
Kai Yang
Keyword(s):  
Direct Method ◽  
Three Dimensional ◽  
High Order ◽  
Two Dimensional ◽  
Boundary Integrals ◽  
Third Order ◽  
Curved Boundary ◽  
Plane Method ◽  
The Third ◽  
Projection Plane

Boundary element method (BEM) is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expanding the geometry quantities at the field point as Taylor series. New analytical formulas are derived for geometry quantities defined on the curved line/plane, and unified expressions are obtained for both two-dimensional and three-dimensional problems. For the two-dimensional boundary integrals, analytical expressions for the third-order derivatives are derived and are employed to verify the complex-variable-differentiation method (CVDM) which is used to evaluate the high order derivatives for three-dimensional problems. A few numerical examples are given to show the effectiveness and the accuracy of the present method.

scholarly journals Plastic waste to fuels by hydrocracking at mild conditions

2021 ◽  
Vol 7 (17) ◽  
pp. eabf8283
Author(s):  
Sibao Liu ◽  
Pavel A. Kots ◽  
Brandon C. Vance ◽  
Andrew Danielson ◽  
Dionisios G. Vlachos
Keyword(s):  
Direct Method ◽  
Acid Sites ◽  
Liquid Fuels ◽  
High Yield ◽  
Tandem Catalysis ◽  
Hy Zeolite ◽  
Environmental Threat ◽  
Single Use ◽  
Initial Activation ◽  
A Direct Method

Single-use plastics impose an enormous environmental threat, but their recycling, especially of polyolefins, has been proven challenging. We report a direct method to selectively convert polyolefins to branched, liquid fuels including diesel, jet, and gasoline-range hydrocarbons, with high yield up to 85% over Pt/WO3/ZrO2 and HY zeolite in hydrogen at temperatures as low as 225°C. The process proceeds via tandem catalysis with initial activation of the polymer primarily over Pt, with subsequent cracking over the acid sites of WO3/ZrO2 and HY zeolite, isomerization over WO3/ZrO2 sites, and hydrogenation of olefin intermediates over Pt. The process can be tuned to convert different common plastic wastes, including low- and high-density polyethylene, polypropylene, polystyrene, everyday polyethylene bottles and bags, and composite plastics to desirable fuels and light lubricants.

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