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Abstrak :
ABSTRACT Resistivity surveying is commonly interpreted in term of one dimensional approach, which is based on the assumption that the subsurface consists of a system of parallel, horizontal, homogeneous and isotropic layers. Very often this assumption amounts to a gross simplification of the actual geology. Consequently, 1D-interpretation can not overcome equivalence problems, lateral and vertical in-homogeneity, as well as it can not determine more realistic subsurface structures. However, if we use a two-dimensional approach by making provision for the variation of resistivity in two directions, x and z direction or y and z direction (two-dimensional interpretation), and by assuming that no resistivity variation along the third orientation (i.e. y or x axes), a more realistic model of the subsurface can be constructed. Fundamental equations, finite-difference equations, numerical algorithm and modification of Fortran computer codes, based on Dey's codes, are described in this Masters Thesis. The simulations of 2D-resistivity modelling for equivalence problems, lateral and vertical in-homogeneity, as well as case study of 2D-resistivity modelling in determining resistivity structures in Ulubelu Geothermal Prospect, Indonesia, are also presented. It has shown that the limitations of 1D-interpretation can be overcome by using the two-dimensional approach.

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Skripsi ini merupakan pemodelan aliran sungai secara dua dimensi yang berupa kecepatan arah x, kecepatan arah y, dan kedalaman air. Ketiga variabel ini dihitung dengan persamaan massa dan momentum. Persamaan dasar kekekalan massa dan momentum diturunkan dahulu agar diperoleh bentuk dua dimensinya. Kemudian bentuk differensialnya dimodelkan dengan metode beda hingga forward difference. Perhitungan dilakukan untuk kondisi sungai yang steady maupun unsteady. Untuk kondisi unsteady, digunakan metode numerik Runge Kutta orde 4. Rumus yang diperoleh ini akan dimasukkan ke dalam listing program visual basic agar memudahkan pemodelan dalam tahap perhitungan, sehingga inilah yang disebut sebagai Program Pemodelan Beda Hingga.

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The focus of this study is developing two dimensional river current that consists of velocity in x direction, velocity in y direction, and depth of water. These three variables can be computed from the continuity and momentum equation. Firstly we have to differentiate the equations to get two dimensional forms. Then, it can be modeled with forward finite difference method. Computation is done for steady and unsteady state. For unsteady state, 4th order Runge Kutta is used. The equation is inputed to visual basic program listing to make the computation in modeling process easier, so this is called Finite Difference Model Program.

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Rain produces both,surface run off and base flow.In this journal , we will be discussing about developing a software for surface run off modelling based on the Saint Venant equation,using MacCormak 2D method......

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Pesticide transport and transformation were modeled in soil column from the soil surface to goundwater zone...

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This book provides an elementary introduction to some one-dimensional fluid flow problems involving shock waves in air. The differential equations of fluid flow are approximated by finite difference equations and these in turn are numerically integrated in a stepwise manner. Artificial viscosity is introduced into the numerical calculations in order to deal with shocks. The presentation is restricted to the finite-difference approach to solve the coupled differential equations of fluid flow as distinct from finite-volume or finite-element methods. This text presents the results arising from the numerical solution using Mathcad programming. Both plane and spherical shock waves are discussed with particular emphasis on very strong explosive shocks in air.

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ABSTRAK
Intrusi air laut merupakan salah satu masalah kualitas air tanah yang dapat dimodelkan secara matematika. Model matematika diformulasikan dalam bentuk persamaan diferensial parsial yang kemudian solusi persamaan dapat dilakukan secara numerik. Tujuan utama dari penelitian ini adalah menyimulasikan secara numerik intrusi air laut pada suatu akuifer terkekang. Untuk menyimulasikan intrusi air laut, diperlukan persamaan aliran air tanah dependent-density atau persamaan air tanah yang mengakomodir perubahan massa jenis terhadap ruang dan waktu. Penelitian ini menggunakan persamaan aliran air tanah dependent-density yang pernah dikembangkan oleh Kurnia (2012). Persamaan lain yang diperlukan adalah persamaan transpor adveksidispersi dan gradien perubahan massa jenis terhadap perubahan konsentrasi. Diskritasi persamaan diferensial menggunakan metode Finite-Difference melalui skema Alternating Direction Implicit (ADI). Simulasi model dilakukan dengan menyusun program pada bahasa Visual Basic for Application (Excel-VBA). Model diperlakukan dengan 2 kondisi simulasi yaitu tanpa dan dengan pemompaan akuifer. Hasil akhir simulasi menggambarkan kondisi model sebelum dan setelah intrusi air laut sesuai dengan kodisi teoritisnya.

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ABSTRACT
Seawater intrusion is one of the groundwater quality problems which can be simulated as a mathematical model. The mathematical model is formulated as the partial differential equation (PDE) and the solution of the PDE is obtained numerically. The Main objective of this research to simulate seawater intrusion phenomena numerically in the confined aquifer. Dependent-density groundwater flow model is necessary to simulate seawater intrusion phenomena. This research employs the dependent-density groundwater flow model which developed by Kurnia (2012). The other equations to complete simulation are advection-dispersion transport model and the gradient of the changes of fluid density to the changes of concentration constituent. Discretization of PDE is conducted using the Finite-Difference method through Alternating Direction Implicit (ADI) scheme. Simulation is conducted by developing computer programming. Visual Basic for Application (Excel-VBA) is chosen for this research. There are 2 conditions of simulation follows without and by pumping aquifer. The final result of simulation describes both of the model condition, before and after pumping aquifer are appropriate to the theoretical condition.

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Struktur Electromagnetic Band Gap (EBG) pada aplikasi antena mikrostrip bisa mencegah munculnya gelombang permukaan yang menyebabkan karakteristik antena mikrostrip menjadi tidak optimal. Gelombang permukaan timbul ketika substrat yang digunakan memiliki konstanta dielektrik lebih besar dari satu (er > 1). Teknik EBG ini dapat digunakan untuk memperbaiki karakteristik antena mikrostrip. Dalam tesis ini, masalah medan magnet dan medan listrik pada struktur EBG suatu material dapat diformulasikan ke dalam bentuk persamaan Maxwell dalam variabel diferensial dan integral. Persamaan Maxwell dalam struktur EBG tersebut dipecahkan dengan menggunakan beberapa metode numerik yaitu dengan menggunakan metode transfer matriks dan metode Finite Difference Time Domain (FDTD). Tak seperti metode lain yang biasa digunakan, metode transfer matriks ini tidak hanya menginformasikan struktur EBG tapi juga untuk mengetahui koefisien transmisi dan refleksi. Metode ini dibatasi untuk stuktur EBG pola kubik simetri. Persamaan-persamaan medan magnet dan medan listrik dari pemodelan yang didapat dengan menggunakan metode transfer matriks ini lebih sederhana karena mereduksi variabel-z dari medan magnet dan medan listrik sehingga menjadi lebih mudah dalam perhitungan atau proses numerik. Metode transfer matrik yang dihasilkan selanjutnya dibandingkan dengan metode FDTD dari algoritma Yee. ......Eleclromagnetic Band Gap (EBG) structure in application of microstrip antenna can be overcome of surface wave which causes microstrip antenna charactcristic becomes not optimal. The surface waves arc excited when the substrate have dielectric constant morc tiran one (er > 1). EBG technique can improve microstrip antenna characteristic. In this thesis, electric and magnetic field in EBG structue can be formulated into the Maxwell’s equations in differential and integral variable. Maxwell’s equations in EBG structure is solved with transfer matrix method. Unlike other methods commonly used this technique gives access to not only EBG structure information but also fransmission and reflection coefficients. This method confined to systems with cubic symmetry.The equations of electric and magnetic field from obtained modeling with transfer matrix method to be simple because its reduce z-variable, so become more easy into numerical calculation. Transfer matrix method had a result is compared with FDTD method from Yee algorithm.

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Penelitian ini mengevaluasi performa dua metode utama untuk menentukan konduktivitas termal pada kuningan dan stainless steel menggunakan Inverse Heat Conduction Problem (IHCP) 2 dimensi: dekomposisi LU dengan batasan dan Algoritma iterasi Conjugate Gradient Method (CGM) dengan Backpropagation Learning. Tujuan penelitian adalah menganalisis dampak variasi material, konfigurasi insulasi, tebakan nilai awal konduktivitas termal, dan daya pemanas terhadap hasil akhir konduktivitas termal. Metode CGM dipilih karena efisiensinya dalam menangani sistem persamaan linier besar, sementara dekomposisi LU efektif untuk matriks pentadiagonal. Simulasi dan eksperimen dilakukan untuk memvalidasi metode ini, dengan variasi daya pemanas dan tebakan awal nilai konduktivitas termal. Hasil menunjukkan bahwa pada pelat kuningan, prediksi konduktivitas termal simulasi berada diantara 110,157-111,659 dengan kesalahan absolut maksimum sebesar 0,76% dan prediksi konduktivitas termal eksperimen berada diantara 109,802-111,382 dengan kesalahan absolut maksimum sebesar 1,08% sedangkan pada pelat stainless steel, prediksi konduktivitas termal simulasi berada diantara 13,502-13,933 dengan kesalahan absolut maksimum sebesar 1,99% dan prediksi konduktivitas termal eksperimen berada diantara 13,502-13,951 dengan kesalahan absolut maksimum sebesar 2,16%. Peningkatan daya pemanas tidak mempengaruhi nilai konduktivitas termal, tetapi tebakan awal konduktivitas termal mempengaruhi jumlah iterasi yang dibutuhkan untuk mencapai nilai konduktivitas termal yang akurat. Penelitian ini juga menyoroti batasan seperti analisis dalam kondisi steady-state dan skala laboratorium eksperimen. Rekomendasi untuk penelitian mendatang mencakup pengaturan sistem tertutup pada eksperimen untuk mengontrol suhu lingkungan serta penerapan algoritma machine learning guna meningkatkan akurasi prediksi konduktivitas termal material. Secara keseluruhan, penelitian ini menegaskan bahwa metode yang digunakan efektif dalam memprediksi konduktivitas termal kuningan dan stainless steel, meskipun material dengan konduktivitas rendah cenderung memiliki kesalahan yang lebih besar dalam pengukuran dengan metode IHCP. ......This research evaluates the performance of two primary methods for determining thermal conductivity in brass and stainless steel using the 2-dimensional Inverse Heat Conduction Problem (IHCP): LU decomposition with constraints and the iterative Conjugate Gradient Method (CGM) with Backpropagation Learning. The study aims to analyze the impact of material variation, insulation configuration, initial thermal conductivity guesses, and heating power on the final thermal conductivity results. CGM was chosen for its efficiency in handling large linear equation systems, while LU decomposition is effective for pentadiagonal matrices. Simulations and experiments were conducted to validate these methods, with variations in heating power and initial thermal conductivity guesses. The results show that for brass plates, simulated thermal conductivity predictions range between 110.157 and 111.659 with a maximum absolute error of 0.76%, and experimental predictions range between 109.802 and 111.382 with a maximum absolute error of 1.08%. For stainless steel plates, simulated thermal conductivity predictions range between 13.502 and 13.933 with a maximum absolute error of 1.99%, and experimental predictions range between 13.502 and 13.951 with a maximum absolute error of 2.16%. An increase in heating power does not affect the thermal conductivity values, but the initial thermal conductivity guesses influence the number of iterations required to achieve accurate thermal conductivity values. This research also highlights limitations such as the steady-state analysis and the laboratory-scale experiments. Recommendations for future research include implementing a closed-system setup in experiments to control ambient temperature and applying machine learning algorithms to improve the accuracy of thermal conductivity predictions. Overall, this study confirms that the methods used are effective in predicting the thermal conductivity of brass and stainless steel, although materials with low conductivity tend to have higher measurement errors with the IHCP method.