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We consider the shallow water equations along channels with non-uniform rectangular cross sections with source terms due to bottom topography, channel width, and friction factor. The system of equations consist of the mass and momentum conservation equations. We have two main goals in this paper. The first is to develop a numerical method for solving the model of shallow water equations involving those source terms. The second is to investigate effects of friction in water flows governed by the model. We limit our research to the flows of one-dimensional problems. The friction uses the Manning's formula. The mathematical model is solved numerically using a finite volume numerical method on staggered grids. We propose the use of this method, because the computation is cheap due to that no Riemann solver is needed in the flux calculation. Along with a detailed description of the scheme, in this paper, we show a strategy to include the discretization of the friction term in the staggered-grid finite volume method. Simulation results indicate that our strategy is successful in solving the problems. Furthermore, an obvious effect of friction is that it slows down water flows. We obtain that great friction values lead to slow motion of water, and at the same time, large water depth. Small friction values result in fast motion of water and small water depth.

Floods, which cause a lot of damage, are a natural phenomenon that often occurs during the rainy season. Flood occurs because the discharge entering the channel exceeds the channel capacity. If the discharge data in the upstream area that will enter the channel is known, we can determine the flow behavior in the downstream area using a mathematical model. In this study, we proposed using simplified Saint Venant equations to simulate the flow routing in a prismatic channel with a rectangular section. This model is solved numerically using the finite difference method. Here, the numerical scheme used succeeds in simulating the flow behavior in the channel due to the discharge entering it. The simulation results show that the discharge entering the channel will propagate downstream with decreasing discharge quantity. Information on the amount of discharge at locations along the channel is useful as supporting data for flood control and prevention systems that will be conveyed to residents along the channel.Keywords: flood routing; prismatic channel; Saint Venant Equations; finite difference method. AbstrakBanjir yang menimbulkan banyak kerusakan merupakan fenomena alam yang sering terjadi pada musim hujan. Banjir terjadi karena debit yang masuk ke dalam kanal melebihi kapasitas kanalnya. Jika data debit di daerah hulu yang akan masuk ke dalam kanal diketahui, maka kita dapat menentukan perilaku aliran di daerah hilir dengan menggunakan model matematika. Dalam studi ini, kami mengusulkan untuk menggunakan persamaan Saint Venant yang disederhanakan untuk mensimulasikan penelusuran aliran pada saluran prismatik dengan penampang persegi panjang. Model ini diselesaikan secara numerik dengan menggunakan metode beda hingga. Di sini, skema numerik yang digunakan berhasil mensimulasikan perilaku aliran pada saluran akibat debit yang masuk. Hasil simulasi menunjukkan bahwa debit yang masuk ke saluran akan merambat ke hilir dengan kuantitas debit yang semakin berkurang. Informasi jumlah debit di lokasi sepanjang saluran ini berguna sebagai data pendukung pada sistem pengendalian dan pencegahan banjir yang akan disampaikan kepada penduduk di sepanjang kanal.Kata kunci: penelusuran banjir; saluran prismatik; persamaan Saint Venant; metode beda hingga.

Both teachers and students have carried out various studies on creativity. In general, creativity research is associated with solving mathematical problems. In this research, we want to reveal the characteristics of the creative mathematics teacher subject as another finding in uncovering the stages of the teacher's creative thinking. The results of this study found that creative teachers can observe, ask questions, reason, make analogies and try. Keywords: [observing, asking, reasoning, analogizing, and trying]