A NOTE ON DOWNWARD CONTINUATION OF GRAVITY

Geophysics ◽  
1954 ◽  
Vol 19 (1) ◽  
pp. 71-75 ◽  
Author(s):  
César A. Trejo
Keyword(s):  
Finite Differences ◽  
Downward Continuation ◽  
Upward Continuation ◽  
Finite Differences Method ◽  
Downward Continuation Of Gravity

Comparing calculated and exact values in an ideal example, it is shown that Peters’ proposed method of downward continuation of gravity is far less suitable than a combination of Peters’ procedure for upward continuation and a finite differences method for downward continuation. It is shown also how Peters’ method can be substantially improved by considering only the closest values in the downward step of a continuation process.

scholarly journals 3-dimensional analysis of holographic memories based on photopolymers using finite differences method

2006 ◽  
Author(s):  
Sergi Gallego ◽  
Manuel F. Ortuño ◽  
Cristian Neipp ◽  
Andrés Márquez ◽  
Augusto Beléndez ◽  
...  
Keyword(s):  
Dimensional Analysis ◽  
Finite Differences ◽  
3 Dimensional ◽  
Finite Differences Method ◽  
Holographic Memories

On the choice of CFD codes in the design process of planing sailing yachts

2009 ◽  
Author(s):  
Jérémie Raymond ◽  
Jean-Marie Finot ◽  
Jean-Michel Kobus ◽  
Gérard Delhommeau ◽  
Patrick Queutey ◽  
...  
Keyword(s):  
Free Surface ◽  
Design Process ◽  
Finite Differences ◽  
Potential Flow ◽  
Surface Condition ◽  
Cpu Time ◽  
Free Surface Condition ◽  
Finite Differences Method ◽  
Non Linear ◽  
Ranse Solver

The discussion is based on results gathered during the first two years of a 3 years research program for the benefits of Groupe Finot-Conq, Naval Architects. The introduction presents the objectives of the program: Setting up a practical method using numerical and experimental available tools to design fast planing sailing yachts. The aim of this paper is to compare advantages and disadvantages of four different kinds of CFD codes which are linear and non-linear potential flow approach, RANSE solver using finite differences method and RANSE solver using volume of fluid method. The Fluid Mechanics Laboratory of the Ecole Centrale de Nantes (France) has developed those three approaches so those homemade codes will be used for this study. The first one is REVA, a potential flow code with a linearised free surface condition. ICARE is a RANSE solver using finite differences method with a non linear free surface condition. It is extensively used for industrial projects as for sailing yachts projects (ACC for example). ISIS-CFD is a RANSE solver using finite volume method to build the spatial discretization of the transport equations with unstructured mesh. The latter is able to compute sprays for fast planing ships but is also the slower in terms of CPU time. In addition, we had the opportunity to test FS-FLOW which is a potential flow code with a non linear free surface condition distributed by FRIENDSHIP CONSULTING. Numerical results for the four codes are compared with the other codes' results as with tank tests data. Those tank tests were made using captive model test technique on two Open60' models. Reasons of the choice of the captive model technique are explained and experimental procedures are briefly described. Comparisons between codes are mainly based on the easiness of use, the cost in CPU time and the confidence we can have in the results as a function of the boat speed. Flow visualizations, pressure maps, free surface deformation are shown and compared. Analysis of local quantities integrated or by zone is also presented. Results are analyzed focusing on the ability of each code to represent flow dynamics for every speed with a special attention to high speeds. The practical question raised is to know which kind of answers each code can bring in terms of tendencies evaluation or sensitivity to hull geometry modifications. The main goal is to be able to judge if those codes are able to make reliable and consistent comparisons of different designs. Conclusion is that none of the codes is perfect and gather all the advantages. It is still difficult to propose a definitive methodology to estimate hydrodynamic performances at every speed and at every stage of the design process. Knowing each code limitations, it appears more coherent to use each of them at different stages of the design process: the quickest and less reliable to understand the main tendencies and the longest and more precise to validate the final options.

scholarly journals Pemodelan Hidrogeologi Cekungan Airtanah Samarinda-Bontang Segmen Penajam Dalam Upaya Konservasi Airtanah Berbasis Cekungan, Kabupaten Penajam Paser Utara, Provinsi Kalimantan Timur

2019 ◽  
Vol 2 (1) ◽  
pp. 13
Author(s):  
Arizatur Reza Wicaksono ◽  
Thomas Triadi Putranto ◽  
Reddy Setyawan
Keyword(s):  
Finite Differences ◽  
Finite Differences Method

Peraturan Menteri ESDM No. 7 Tahun 2017 tentang Cekungan Airtanah pasal 2 ayat 3 menyebutkan bahwa sistem pengelolaan airtanah didasarkan pada Cekungan Airtanah, namun di Indonesia masih banyak daerah-daerah yang masih menggunakan sistem pengelolaan berbasis sumur produksi yang dibatasi pada wilayah administrasi. Tujuan dari penelitian ini adalah untuk membuat model numerik pada Cekungan Airtanah (CAT) Samarinda segmen Penajam berdasarkan model konsep yang dibuat berdasarkan data-data di lapangan. Model nantinya akan digunakan sebagai acuan dalam menentukan rekomendasi terkait konservasi airtanah dari hasil simulasi model. Model numerik dibuat dengan memasukkan parameter-parameter hidrogeologi. Diskritisasi geometri dan iterasi berdasarkan metode beda hingga (finite differences method). Simulasi model yang dilakukan berdasarkan prediksi debit pemompaan hingga 20 tahun kedepan. Hasil kalibrasi model didapatkan nilai RMSE sebesar 0,75 m, ME sebesar 0,1 m, dan MAE sebesar 0,63 m, dengan nilai koefisien korelasi sebesar 0,944. Zona konservasi airtanah dibuat dengan mengkombinasikan persentase penurunan airtanah berdasarkan simulasi model pada skenario terburuk, daerah imbuhan dan lepasan, dan nilai daya hantar listrik di daerah penelitian. Didapatkan 4 (empat) prediksi zona konservasi airtanah, yaitu: zona perlindungan airtanah seluas 107,69 km2 (26,39%), zona aman seluas 229,35 km2 (56,21%), zona rawan seluas 60,35 km2 (14,79%), dan zona kritis seluas 10,64 km2 (2,61%).

A MODIFIED FINITE DIFFERENCES METHOD FOR ANALYSIS OF ULTRASONIC PROPAGATION IN NONHOMOGENEOUS MEDIA

2010 ◽  
Vol 18 (01) ◽  
pp. 31-45 ◽  
Author(s):  
LUCIANO ALONSO RENTERIA ◽  
JUAN M. PEREZ ORIA
Keyword(s):  
Helmholtz Equation ◽  
Finite Differences ◽  
Computational Cost ◽  
Industrial Applications ◽  
Ultrasonic Waves ◽  
Nonhomogeneous Media ◽  
Finite Differences Method ◽  
High Gradients ◽  
Ultrasonic Propagation ◽  
Homogeneous Media

The propagation of ultrasonic waves is generally studied in homogeneous media, although in certain industrial applications the conditions of propagation differ from the ideal conditions and the predicted results are not valid. This work is focused on the resolution of the Helmholtz equation for the study of the ultrasonic propagation in nonhomogeneous media. In this way, the solution of the Helmholtz equation has been obtained by means of Finite Differences, using a nonconventional scheme that substantially improves the results obtained with other techniques such as standard Finite Differences or Finite Elements. Moreover, it decreases the computational cost in the calculation of the coefficients about 85%. The effects on the ultrasonic echoes in propagation environments with high gradients of propagation's speed have been analyzed by simulation using the method presented, and the results obtained have been experimentally validated through a set of measurements.

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